Volumen 8 (2023): Edición 1 (January 2023)

This paper takes the degree of debt concentration and product market competitive advantage as intermediary variables to explore the internal mechanism of the impact of CSR fulfilment on firm debt risk. It is found that the fulfilment of CSR can reduce the debt risk of firms by dispersing the degree of debt concentration and enhancing the competitive advantage of product market. The mediating effect of the degree of debt concentration has a direct impact on the competitive advantage of a product market and is particularly obvious in private firms and firms in the eastern region of China.

As the primary killer of health, the class of infectious diseases is the greatest threat to humanity. At present, international methods of studying the large-scale spatial transmission of sudden infectious diseases from the perspective of dynamics can be divided into two categories. On the one hand, top international biomedical and medical teams discuss the restraining effects of some prevention and control strategies on infectious diseases, such as smallpox, malaria, hand, foot and mouth disease and pandemic influenza, from the perspective of pragmatism. On the other hand, researchers in theoretical physics and network science tend to use compound population network models to explore the internal dynamic mechanism of spatial transmission of infectious diseases. This paper establishes a Lotka–Volterra dispersal predator–prey system in a patchy environment. It shows the existence of model boundary equilibria and asymptotic stability under an appropriate condition. This paper adopts the method of global Lyapunov function and the results of graph theory. We also consider a predator–prey dynamical model in a patchy environment, where the prey and predator individuals in each compartment can travel among n patches.

This article describes and illustrates Paris panxiensis (J. L. Liu) Y. Yuan & J. L. Liu from a morphological perspective, based on field survey, indoor potting and garden cultivation, and observations gleaned from these activities. This variety is closely related to P. delavayi Franch, P. daliensis H. Li et V. G. Soukup, P. lihengiana G. W. Hu & Q. F. Wang and P. polyphylla Smith var. stenophylla Franch, but differs from these in having the following characteristics: flower parts with a basic number of 4–8, petals far shorter than sepals, linear-virgate, bottom linear, gradually thickening upward, erect, never extend or curved, apex rounded or obtuse, and connectivum projecting.

The influence of model deformation on the transmission characteristics in unilateral finline, antipodal finline and bilateral finline is discussed using edge-based finite element method (FEM). The deformation is considered with respect to the eight boundaries of the model, and their amplitude is set to 0.01–0.05; the transmission characteristics include the cutoff wavelength characteristics of the dominant mode and the single-mode bandwidth characteristics. The results show a decreasing trend when the vacuum area is deformed, while they show a variety of possibilities when the loading region is deformed. These numerical results have strong guiding significance for the influence of the deformation of finlines on the overall device.

This paper has collected more than one hundred papers about resilience at home and abroad, summarised and analysed the meaning and evaluation methods of resilience and then summarised the key issues. Through research on these papers, we found that the current evaluation method for the water supply system seismic resilience is divided into two aspects: on the one hand, it’s based on the seismic performance of water supply system, where the system itself evaluates the resilience absorbs the earthquake resistance level. On the other hand, the assessment is based on the post-earthquake recovery ability of the water supply system, namely the recovery time, recovery degree, recovery path and the resilience level of resources input. Based on past seismic safety of the water supply system and research on post-earthquake recovery ability, the meaning of water supply system in seismic resilience should include two aspects of seismic safety and post-earthquake recovery ability. From using the seismic safety evaluation method also and post-earthquake recovery ability in two angles, this paper gives a comprehensive multiple evaluation index framework of the evaluation model and points out that water system earthquake state resilience evaluative criteria and the requirements of the current seismic code should match.

Although the traditional recurrent neural network (RNN) model can cover the time information of the whole sentence theoretically, the gradient is dominated by the short-term gradient, and the long-term gradient is very small, which makes it difficult for the model to learn the long-distance information, and thus the effect of RNN on long text sentence recognition is poor. The long short-term memory network (LSTM) introduces the gate mechanism, especially the forgetting gate, which improves the disappearance of the gradient of RNN. Therefore, LSTM can store long text information and remove or increase the ability of information interaction by adding gate structure, which has natural advantages for long text processing. Based on the word vector matrix of GloVe model, on the open-source comment sentiment140 data set, we use the TensorFlow framework to construct the LSTM neural network and divide the data into the training set and test set based on the ratio of 4:1, design and implement the sentiment analysis published by Twitter users based on LSTM model, and then propose the bidirectional LSTM (Bi-LSTM) sentiment analysis method. The experimental results show that the accuracy of bidirectional LSTM is higher than that of unidirectional LSTM in sentiment analysis.

The quality of the milled surface affects the performance of the affiliated workpiece, since it plays a vital role in determining the precision of the geometry and duration of service time. In this paper, a modified convolution recurrent neural network (CRNN) is proposed to effectively predict the surface quality of the end milling workpiece. First, the validated features of milling force data in the machining process are extracted based on the proposed artificial network model. Second, a modified CRNN model is constructed by merging residual neural network with the help of bidirectional long- and short-term memory as well as attention mechanism. Third, the model’s weight is optimised according to the changes in the loss function and directional propagation principle, which significantly improves the effectiveness of the proposed model. Finally, the actual experiment is carried out on a 5-axis milling centre to validate our model. Also, the surface quality predicted by the CRNN model is in good accordance with the experimental result. In our experiment, an accuracy of 98.35% is achieved, which is a significant improvement compared to the classic CRNN method.

This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed.

At present, the economic benefits of double inlet and double outlet ball mills, which are commonly used in coal-fired power plants, need to be improved. Based on this, this paper explores the factors influencing the output of double inlet and double outlet ball mill by establishing the output system of double inlet and double outlet ball mill. By analyzing the influence factors of the output of double inlet and double outlet ball mill, and combining with system dynamics, the dynamic model of double inlet and double outlet ball mill output system is established, and SPSS is used to fit the model data with the real data. The fitting degree is above 0.8, and the authenticity is high. The simulation results show that the impact energy of barrel grinding, the grinding powder fineness, and the pressure ratio in the ball mill affect the output of double inlet and double outlet ball mill according to certain relations. Finally, the research in this paper provides theoretical and technical support for improving the economic benefits of double inlet and double outlet ball mills.

The Belt and Road (B&R) is a major initiative and vision for China and the world to jointly create prosperity. Based on the data of resident credit card consumption in 291 cities in China from 2011 to 2016, this article establishes a consumption relationship model for cities along the B&R to investigate the impact of the initiative on resident consumption. Through the DID model, there are the following findings. First, the B&R Initiative has a significant positive impact on the resident consumption in cities along the route. Second, the B&R Initiative has a significant effect on the promotion of various industries, and the crowding-out effect of government investment is relatively small. The research conclusions are of reference significance for policy formulation on the specific practice path and detailed measures of the B&R Initiative.

In this article, a three-axis attitude manoeuvre spacecraft consisting of a central rigid body and a rotating solar array is studied. The rotating solar array is considered a disturbance to the spacecraft. In the design of the controller, the coupled terms and the rotating solar array are considered a disturbance. The improved extended state observer is proposed by combing the sliding mode observer with the originally extended state observer to estimate the disturbance. The sliding mode control method is adopted to adjust the attitude of the spacecraft. Numerical simulations are presented to demonstrate the outstanding performance of the present observer.

The efficiency of support vector machine in practice is closely related to the optimal selection of kernel functions and their hyper-parameters. A novel kernel, namely the arctangent kernel, is proposed in this paper. Compared with the Gaussian kernel, the new proposed kernel has a quick similarity descent in the neighborhood of the inspection sample and a moderate similarity descent toward the infinity of the inspection sample. The experimental results on two simulated data sets and some UCI data sets show that the new proposed kernel function has better effectiveness and robustness compared with the polynomial kernel, the Gaussian kernel, the exponential radial basis function, and the former proposed kernel with moderate decreasing.

This paper proposed an approach for the identification of mutation mechanisms of breast cancer in women in four member countries of the Middle East Cancer Consortium i.e. Egypt, Jordan, Cyprus and Israel (Arabs and Jews). We set up multistage models including both gene mutation and the clonal expansion of intermediate cells. We fit the data-set related to the incidence of female breast cancer in the four member countries. Our simulation results show that the maximum number of driver mutations of breast epithelium stem cells of Egyptian women is 13, whereas there are 14 driver mutations in the genome of stem cells of female patients in Jordan, Cyprus and Israel (Arabs and Jews). In addition, the 3, 10, 5, 5 and 4 stage models are the optimal ones for the tumorigenesis of females in Egypt, Jordan, Cyprus, Israel (Arabs) and Israel (Jews), respectively. The genomic instability is caused by first three driver mutations.

With the development of China’s economy, the total area of public buildings is continuously increasing, and higher energy consumption in this field is gradually becoming prominent. In order to improve this situation, China has been working on energy savings in public buildings since 2007. Energy-saving models and energy policies have become the lifeline of sustainable energy development. Furthermore, the energy-saving renovation of public buildings, as a key project, has attracted the attention of governments and scholars. In the report of the 18th National Congress of the Communist Party of China, energy conservation and emission reduction were given a prominent place. The 13th Five-Year Plan (2016-2020) aims to further promote China’s energy conservation work. On the one hand, administrative and legal measures should be taken to strengthen energy conservation. On the other hand, it is necessary to speed up the establishment of a long-term market-based energy-saving mechanism and to rely on market forces to remove various obstacles to energy conservation. Energy performance contracting (EPC) is a practical and effective method applied in energy conservation. Therefore, this research aims to put forward a relatively perfect energy-saving risk management system for EPC public building projects based on analysis of the factors influencing investment risks of energy-saving projects and the use of quantifiable risk management models, thus providing some theoretical support for the risk decision-making of energy service companies.

The multifractal theory is applied in an analysis of bridge disturbance signals with the aim of investigating their nonlinear characteristics, and then the recognisable fault features are extracted from them. By calculating the box dimension and correlation dimension of the bridge disturbance signal, the dimensional characteristics of the disturbance data are analysed to distinguish the health-state of the bridge. Finally, taking the bridge disturbance data as an example, and by using the multifractal spectrum analysis of the disturbance data, it is concluded that the multifractal method can accurately identify the fault state and realise the bridge health monitoring.

More and more attention has been paid to the research on bridge structure health monitoring and state analysis technology, especially the theory and technology of time series analysis based on bridge deflection information. In this paper, multi-fractal de-trend analysis (MF-DFA) is used to analysis the deflection information of bridges. The deformation characteristic parameters can be obtained by the multi-fractal de-trend fluctuation method, which can effectively identify the deformation degree of bridges. The analysis result shows that the multi-fractal de-trend fluctuation analysis method provides the theoretical basis and implementation approach for the health monitoring of the bridge.

In a bid to quantify the sensitivity of envelope enclosure’s design parameters in the dry-hot and dry-cold areas and to provide a reference for the local building performance design, this paper uses ANN modelling which combined with the improved Garson algorithm to calculate the connection weight sensitivity (CWS), the first-order sensitivity (RBD-S1 and DMIM-S1) and the global sensitivity (DMIM-delta) of the design parameters. These parameters were calculated by using different methods in SALib. Through the verification and analysis of the sensitive result, the applicability of the CWS and DMIM-delta was confirmed. Among the design parameters involved in this study, the sum of the sensitive values of S-D, S-N and S-A exceeds 60% in each performance label, and the sum of the sensitive values of WWR_S and WWR_N exceeds 20%. The performance design of envelope enclosure in this area requires applying reasonable shading components and appropriate optimisation of the North and South of WWR. After the sensitivity analysis process, the calculation efficiency of the model can be improved as far as possible without reducing the accuracy of the model in the later simplified calculation and multi-objective optimisation. The building performance simulation model has a high degree of non-linearity, and the interpretability of the model can be enhanced through the sensitivity analysis process. Although the internal calculation process is unknowable, the perception of the results caused by the input parameters is significantly enhanced.

The article applies mathematical calculus modeling to analyze the force of shot put. We emphatically analyzed the relationship between the angle of the shot and the initial velocity and calculated the motion trajectory equation of the shot put. The above research results are used to assist in the analysis and help improve the teaching performance of sports shot put. The study found that different forces have different effects on the horizontal displacement of the shot. Under the comprehensive force analysis, the horizontal velocity gradually decreases with time, and under the gravity analysis, the horizontal velocity of the shot is constant. The horizontal displacement of the shot put is related to the shooting angle and initial speed. Under the comprehensive force analysis, the influence of air resistance and buoyancy on the throwing distance is different due to the different combinations of shooting angle and initial speed.

This article uses fifth-order nonlinear differential equations to describe the dynamic process of electrical automation control systems. This method first derives the equivalent system of the nonlinear fuzzy global system and then uses the orthogonal polynomial series expansion technique and its integral operation matrix. The local manifold at the dominant unstable equilibrium point of a single-machine infinite-bus system after a failure described by a two-dimensional quadratic nonlinear differential equation is calculated, and the stability boundary of the power system is obtained. The research results show that the output frequency fluctuation of the electrical automation control system is small after the algorithm is adopted, and the intelligent control system can accurately diagnose and warn the electrical faults. The system can meet the requirements of online voltage coordinated control.

This paper refers to the Lagrangian mathematical model and the Rackwitz-Fiessler transform model in modeling advanced mathematics applications. In this paper, the Lagrangian interpolation method and Rackwitz-Fiessler transform are used to calculate the correlation coefficient efficiently. The purpose of this algorithm is to speed up the process of probabilistic modeling. This paper uses integral probability transformation to characterize the output's uncertainty by the production's joint distribution function. The purpose of this process is to improve the reliability of the calculation. Through the algorithm analysis, it is found that the method is reasonable and efficient.

The article explores the evolution of regional spatial differences and has important practical significance for promoting the coordinated development of regional tourism. The article analyzes the characteristics of the spatial evolution of the economic tourism pattern from 2010 to 2020. The study found that the development of the regional tourism economy is on the rise, and the development is not balanced. The spatial self-organization of economic development is getting stronger and stronger, and the spatial economic distribution is different. Then this article analyzes the main factors that cause this spatial distribution and proposes corresponding solutions. This provides a theoretical basis for reducing the gap in the tourism economy between regions and promoting the coordinated development of the regional tourism economy.

The article theoretically analyzes the relevant knowledge of shot put in the shot put sports training of colleges and universities. The fractional differential equations are used to analyze the influence of the initial speed and the shot situation on the performance of the shot put. We obtain the joint angles of each stage of the shot throw through experimental design, time-consuming, final speed, limb displacement, shot-put shot speed, height, angle, and other kinematic parameters, and the shot-put motion trajectory of the picture stroke of the relevant action characteristics.

We use the panel data of innovation and entrepreneurship for global spatial autocorrelation and model selection testing. At the same time, we applied the Spatial Dubin Model (SDM) to empirically study the knowledge spillover effects of higher education campuses on regional innovation capabilities. Experimental research found that there are significant spatial differences in the innovation efficiency of universities. Specialized agglomeration can effectively improve the innovation efficiency and scale efficiency of colleges and universities. At the same time, the diversified agglomeration has no obvious effect on the innovation efficiency of colleges and universities. The accumulation of high-tech industries can effectively promote the innovation efficiency of universities. Human capital and opening to the outside world can effectively improve the innovation efficiency of universities.

This article combines the fractional differential theory with the total variation method and applies it to defining cultural industry image color matching. At the same time, we propose a new image color matching denoising model based on fractional partial differential equations. The model achieves simultaneous denoising in the time direction and the spaceplane. Experiments have proved that the fractional partial differential equations method has more advantages than integer-order partial differential equations in denoising and reducing step effects. It can effectively improve the contrast and clarity of image color matching in the cultural industry.

This article applies mathematical probability theory to statistical algorithms to conduct game analysis on the relevant marketing decisions of foreign trade cross-border e-commerce. We build a theoretical framework for the collaborative development of SMEs and cross-border e-commerce platforms. At the same time, build a trustworthy transaction margin mechanism for cross-border e-commerce transactions in a fuzzy market environment. The participation of the blockchain big data platform can promote the development of foreign trade cross-border e-commerce toward a more transparent and healthy partnership.

This article proposes a resonance suppression method for a flexible load servo drive system based on a flexible manipulator's pose transformation. We establish a flexible load servo drive system for the robotic arm based on the continuum vibration theory and the transfer function estimation method. The controller consists of two parts: compensation control and dynamic feedback. The transfer function of the active feedback part is strictly positive and real. At the end of the thesis, the asymptotic stability of the closed-loop system in the neighborhood of the desired position is proved through the linear operator semigroup theory and the LaSalle invariant set principle.

We use the Legendre wavelet method to study nonlinear fractional differential equations. Based on the in-depth study of the characteristics of various fractional-order dynamic system models, this paper designs a system for solving fractional-order differential equations, and we apply them to the anomaly analysis of big computer data. This method can improve the efficiency of big data classification. The results of computer numerical simulation show that the designed algorithm for solving fractional differential equations has high accuracy. At the same time, the algorithm can avoid misclassification and omission in big data analysis.

This article combines ordinary differential equations’ theoretical and practical characteristics to explore how to integrate mathematical modeling ideas in teaching materials and teaching methods. We apply the fractional differential equation algorithm to the mathematical modeling of Terman diffusion. At the same time, the article proposes a framework for obtaining accurate solutions of a class of nonlinear Sinai stochastic models with power-law diffusion through Mittag-Leffler function transformation. In this way, we have obtained great explicit and accurate solutions of some important Mittag-Leffler function power-law diffusion physical processes.

The article first uses the fractional derivative to define a new fractional bounded variation function space. This method constructs the corresponding electronic information image model denoising mask by setting a smaller fractional integration order. The experimental results show that the image denoising algorithm based on fractional integration can not only improve the signal-to-noise ratio of the image compared with the traditional denoising method, but also can better retain the details of the edge and texture of the electronic information image.

If you use simple linear equation classification for big data analysis and classification modeling, the work efficiency is low, and the accuracy is also poor. For this reason, the thesis uses nonlinear differential equations to carry out computer-aided unsteady aerodynamic modeling. Based on the perspective of differential equations, the big data classification technology is studied, and the classification model is established. The article constructs the differential classification mathematical model by establishing the differential equation with second-order delay and the constraint conditions of the model specification set. The article identifies and identifies linear parameters such as characteristic time constants in the aerodynamic model. Research shows that the model can accurately predict unsteady aerodynamic characteristics under different maneuvers.

This paper uses the principle of compressed mapping to discuss the existence and uniqueness of the explicit finite difference method for the fractional diffusion equation with time delay. The Laplace transform method obtains the necessary expression form of the solution. At the same time, the existence theorem and the existence and uniqueness theorem of the solution to the boundary value problem is established. Finally, an example is given to verify the correctness of the conclusion. The experimental results show that the parallel algorithm proposed in this paper agrees with the exact solution.

It is more difficult to give Laplace transform directly in a defined form or derive it by Fourier transform in mathematics teaching. The article gives a solution for solving high exponential series sum by using Laplace transform. With the help of Laplace transform, calculus operations can be transformed into complex plane algebra operations. The application of the algorithm to the option hedging strategy verifies the applicability of the algorithm proposed in this article.

This article uses the radial basis function artificial neural network and the MATLAB toolbox to study the vibration control of civil engineering structures. The article proposes a dynamic structure design method based on a generalized radial basis function neural network. Furthermore, the RBF neural network theory is used to optimize the structure-related controller parameters in geotechnical engineering. The research results show that RBF neural network can more accurately predict the vibration response of civil engineering. It can effectively solve the time lag problem in vibration control.

The successful implementation of the robot teleoperation system has greatly improved the ability of remote robots. The force feedback technology is applied to the teleoperation system. On the one hand, the main operator manipulates the operator’s related movement information to the target robot; on the other hand, the main hand feeds back the force situation of the target robot in the remote control to the operator. From the robot under the control of the system can more accurately complete the task, with a higher work efficiency. Teleoperation system with force feedback function generally adopts bilateral control, the master and slave end of the system have a certain delay in the transmission process, it makes the stability of the system destroyed. This paper uses a two-port network to simulate the communications link of the teleoperation system as a lossless transmission line, solves the stability problem of teleoperation systems with force feedback in the presence of time delay effectively. Experimental simulation results show that this method can guarantee a higher stability of the system..

Because the current sports group competition middle school students’ motion video recognition is complicated, the article uses Lagrangian mathematical equations to classify the motion videos. Based on the spatial smoothness of the flicker parameter function, this paper proposes a Lagrangian mathematical method for detecting local motion regions. The research results show that the motion differential equation and numerical calculation method of the video derived in the article are correct.

The article applies mathematical statistics to the dynamic analysis of the demand for talents in large companies. Prediction of the overall demand for talents through the use of deep learning models. We use the theory of diminishing marginal utility to solve the degree of enterprise human resource investment under each index. Based on the analysis of traditional human resource management methods, this paper uses the three-dimensional fuzzy model to construct a new three-dimensional fuzzy model of human resource management model. The research found that the algorithm proposed in this paper can improve the quality of data training and improve the matching of people and posts.

We propose a feature extraction method based on the Kmeans algorithm based on the text characteristics in the English translation corpus. The article first uses a sparse autoencoder unsupervised learning method to reduce dimensionality. It then uses the Kmeans clustering algorithm for text clustering. The experimental results prove that the text features extracted by the sparse autoencoder based on the Kmeans algorithm can be used for English translation corpus knowledge clustering to achieve automatic integration. And this method can effectively solve the problems of high-dimensional, sparse, and noisy texts in the English translation corpus. The algorithm mentioned in the article can significantly improve the accuracy of the clustering results.

This article uses the curve equation model to describe the initial value problem of differential equations in BIM project management. A new set of rolling curve-solving models is established for step-aligning in BIM project management. Based on the premise that the differential equation can be solved numerically, we appropriately simplify or set the required relational functions in the equation. Finally, we use mathematical software to numerically solve the differential equation and obtain the discrete function of the rolling curve. The research shows that the accuracy of the step flatness and the width of the stepped groove formed by the rolling curve of the solution in this paper is better than the original solution.

This article proposes a fault component location method based on graph theory and analyzes the properties of the elements in the fault judgment matrix. We can use the exclusive OR algorithm to determine the faulty section. On this basis, the realization model and algorithm essence of the optimal test set is given. At the same time, we propose an optimal test set design for circuit fault diagnosis based on graph theory. Finally, the realization of the article verified that the method adapts to the flexible operation mode of the active distribution network structure and can accurately determine the fault section.

Many economic variables are interdependent, restrictive, and influential. Finding the law of change between economic variables and influencing factors and expressing this law in mathematical expressions will bring great convenience to forecasting. A statistical analysis method that uses mathematical equations to determine the quantitative relationship between two or more variables. This is more commonly used when estimating and predicting the value of the dependent variable. The article analyzes the data on the National Bureau of Statistics website and uses the method of multiple linear regression to fit the graphs of economic indicators. Finally, the forecast data is analyzed in detail. We evaluated the modeling method of the prediction model and the credibility of the prediction data from a practical level.

This article constructs a nonlinear differential equation model that incorporates non-defective return factors and minimizes the expected cost of the inventory control problem under the cross-border e-commerce overseas warehouse model. Under the dynamic background, the problem of pricing and shop assistant decision-making in the supply chain is studied, and the differential game model is constructed. We use differential game theory to give pricing and store assistance strategies under decentralized and centralized decision-making. At the same time, we designed a contract to achieve supply chain coordination in this context. Numerical examples calculate the optimal return price and optimal order quantity under supply chain coordination.

Visualization software provides powerful numerical calculations for the 3D mathematical modeling process. This paper uses optical motion capture mathematical modeling technology to track and detect dancers’ dance movements in segments in real-time. The research results found that the visual dance choreography system proposed in the article improves the efficiency of posture analysis and real-time analysis improves the quality of teaching. This has played an important role in the digital teaching of dance movements and the development of science.

This article uses mathematical modeling methods to predict the trajectory of a free kick in football. The article calculates the parameters of the ball’s trajectory and quantifies the power of direct free kick shots. The article combines Kalman filter prediction and linear interpolation to supplement the position of the missed ball in the video. The experimental results show that the estimated result of this method is highly similar to the actual flight trajectory of football. This algorithm can be applied in practice.

By establishing common simplified model rules for strollers, the early planning of rapid modeling of new products is realized. We have ergonomically designed the shock-absorbing structure of the stroller. Studies have shown that the vibration damping of the stroller has the greatest relationship with the damping structure of the car body itself. The vibration acceleration monitoring of the cart with the frame damping system found that due to the frame damping system, nylon components are used for isolation between the frame connection parts and between the wheel and the seat pocket so that the nylon can effectively absorb the impact energy.

The paper calculates the nonlinear dynamic differential equation model based on the stiffness of the gear teeth and gives the calculation method of the spring stiffness of the transmission system. Choose the Lyapunov energy function and derive the adaptive law that can make the system asymptotically stable globally. At the same time, we discussed the influence of the phase combination of the coupling shaft’s torsional stiffness and the gears’ meshing stiffness in the multi-stage gear transmission system on the system dynamics. The example calculation shows that the asymptotic method has higher solution accuracy and higher calculation efficiency. This algorithm is a highly versatile analytical solution method.

This article uses SPSS19.0 and AMOS21.0 statistical software to explore the relationship between corporate talent management and corporate performance. We use the structural equation model to quantitatively analyze the human resource management factors that affect logistics performance. Research shows that intellectual capital has a significant positive effect on enterprise innovation performance. The value proposition of employee training to customers and good customer service have an overall positive economic effect. Human capital plays a significant role in driving innovation performance only in the more mature stage of enterprise development.

This article studies the generation of 3D animation simulation based on gray value algorithm and fractal interpolation algorithm. The article uses fractal technology combined with the Diamond-Square algorithm to generate height data and then color it. This algorithm optimizes the 3D animation process. The results show that the algorithm is fast in generating speed and only needs to input a few simple animation parameters to generate different 3D animations.

This article uses a logarithmic growth model to analyze the correlation between the national economy and real estate. It reveals the Granger causality between the national economy and the real estate economy. The results show a long-term equilibrium relationship and a two-way Granger causality between real estate prices and economic growth. Excessive growth in real estate prices will create bubbles and will also drive economic growth backward.

This article first uses a new method of nonlinear combination forecasting based on neural networks to construct a financial crisis early warning model and conduct an empirical study. The drafting article uses Fisher’s second-class linear discriminant analysis and binary logistic regression to establish a three-year early warning model for listed companies before the financial crisis. Empirical research shows that this early warning model applies to various industries. It can play a certain role in predicting and preventing the financial crisis of Chinese companies.

This article uses BIM technology to simulate HVAC in a commercial building. And use fractional differential equations to verify the set temperature, humidity, and other related parameters. The experiment takes an air-conditioned room model as the research object and uses the thermodynamic characteristics to establish a dynamic mathematical model of differential equations. Research shows that the multiple electric heat pump equipment aggregation groups discussed in this article are a good resource for user-side demand response. The air-side flow rate disturbance of the building HVAC has the greatest impact on the heat transfer of the surface cooler. As the air velocity increases, the rate of increase in heat exchange will decrease.

This article applies multiple nonlinear regression methods to establish a forecasting model for the load characteristics of air conditioning in shopping malls at different times. Based on Python data, determine the functional relationship of refrigerant parameters concerning pressure and temperature. The article uses kernel smoothing estimation technology to calculate the room temperature probability density distribution of users participating in DLC to characterize the user’s comfort. The article’s research results show that the average error between the regression analysis results of refrigerant parameters and the reference value is within 1%. This model is suitable for medium and long-term load forecasting. It has high prediction accuracy for the sudden change trend with a turning point.

With the help of fractional differential equations, this article studies the failure morphology, fatigue strength, and fatigue life of corroded reinforced concrete beams under fatigue loading. Studies have shown that the mid-span deflection of low-corrosion reinforced concrete beams is smaller than that of uncorroded reinforced concrete beams. The corrosion-fatigue coupling effect accelerates the fatigue crack growth rate of steel bars. This reduces the fatigue modulus of concrete and causes the stiffness of the beam to degrade. The research results provide a theoretical basis for the fatigue performance evaluation of corroded reinforced concrete beams.

This article takes cross-border e-commerce platform operation receipts as the research object. It uses fractional differential equations to construct a market demand function jointly affected by channel radiation range, price, and price differences. The study results show that the heterodyne effect of cross-border e-commerce guarantees the competitive position of the market incumbents of the cross-border e-commerce platform. The article also illustrates the effectiveness and practicality of the cross-border e-commerce supply and demand fractional differential matching decision-making method.

This article proposes a software fusion processing method for multi-sensor monitoring the Internet of Things based on the fractional differential filtering algorithm. The purpose is to solve the difference between the detection data caused by the difference in each production information sampling node’s equipment performance and working environment. The article applies the above algorithm to the remote detection data fusion processing experiment of the discrete manufacturing system of the Internet of Things. The research found that the algorithm realizes the remote high-precision measurement of the Internet of Things sensor information. The fractional integral operator has high fusion accuracy in remote detection data fusion processing.

This paper applies the Gaussian random field to the mathematical modeling of new-type silicate glass-ceramic trachoma detection. The article established a three-dimensional numerical model of trachoma structure based on the anisotropic random field. Then, the open and closed operations in mathematical morphology are used to obtain the strongly connected boundaries of the new-type silicate glass-ceramic trachoma image. At the same time, the connected domain detection in binary morphology is used to remove the noise to obtain the target image of the silicate glass-ceramic pore. The study found that this method can better meet the requirements of silicate glass-ceramic trachoma measurement than the classic edge detection operator.

Fractional differential equations are one of the important contents of advanced mathematics courses. The article uses fractional differential equations to describe the effects of children’s innovative education courses. Through the qualitative analysis of the basic model, several conditions to ensure the effect of children’s innovative education courses are obtained. At the same time, combined with practical experience, the teaching curriculum case design analyzes the specific application of the fractional differential equation in the effect of children’s innovative education curriculum. Research has found that the fractional differential equation algorithm improves the efficiency of innovation.

This article proposes a nonlinear mental health evaluation model after combining the nonlinear finite element equation with the mental health education of teachers in colleges and universities. We take the “self-concept” in psychology as an order parameter to judge mental health. At the same time, logical thinking is used to guide college teachers to rethink the process of their psychological activities. Research has found that the nature of human psychology is nonlinear. It is feasible to use nonlinear analysis methods to improve the status quo of original data analysis in psychological and behavioral control research.

Sleeping postures are one of the indicators for judging sleep quality and preventing sudden diseases. The sleeping postures not only affect people’s sleep quality but also has great significance for the diagnosis of apnea syndrome and bedsores. To realize and recognize the laying positions, this paper researches the regularized extreme learning (RELM) algorithm to analyze the pressure due to lying positions. Based on this algorithm first, the array pressure sensor is used to obtain the back lying posture pressure image, and the image is pre-processed to complete the extraction of multiple feature values (Geometric features, Energy features, and Colour features). Second, the multi-feature values are normalized and finally, these multi-feature values are trained and predicted by the RELM algorithm. In concluding this, the accuracy of lying posture recognition was the highest, achieving 98.75 percent, this is when 1120 datasets of feature values were used as training data and 160 sets as test data while the hidden nodes were 80. RELM algorithm can overcome the problems of extreme learning (ELM) algorithm, such as slow learning speed and local minimum value, and so on. Therefore, this method can be applied in the scenarios of lying posture recognition.

Targeted at the harmful effects of garment image retrieval at present, a new approach of garment image retrieval featured in satisfactory performance is proposed. In this study, the Grab Cut auto segmentation algorithm is applied first to segment garment images and extract the image’s foreground. And then, the color coherence vector (CCV) and the dominant color method are adopted to extract the color features to conduct garment image retrieval. The experimental data show that the Grab Cut auto segmentation algorithm is capable of extracting the foreground of garment images with either simple or complex background. Meanwhile, the data also indicate that compared with the garment image retrieval by extracting color features using CCV, extracting color features by dominating color method shows both higher accuracy and recall rates.

The article uses ordinary differential to solve inhomogeneous equations by the constructivist learning concept. We use the equivalent equations to study the n-th order non-homogeneous linear ordinary differential equations with constant coefficients and get the method of solving this equation. Then we use the Filippov transformation and comparison theorem to prove the boundedness of all system trajectories. Numerical results show that the calculation formula is effective for solving stiff ordinary differential equations.

The current education system for preschool students has relatively small differences and cannot fully reflect the true mastery of students. The article designs a cognitive system for preschool students’ educational scoring based on mathematical statistics. The article uses the attention vector and knowledge acceptance in children’s teaching as a multi-scale convolution level to analyze the effect of education. The study results found that the evaluation system can analyze the quality of children’s education while also considering children’s learning emotions.

Based on the mathematical equation model of the analytic hierarchy process, the article designs a set of children’s education curriculum scoring management systems. The article clarifies the content of health education curriculum evaluation through investigation and analysis. Optimize the structure of health education curriculum evaluation through continuous refinement of evaluation elements. The article applies the divergence and convergence method to establish secondary indicators through expert evaluation and finds out the problems of the existing children’s education scoring management system through practical application. Finally, relevant opinions were put forward in response to the problem.

This article establishes the actual movement mathematical model of CNC machine tools for the precision processing of jewelry. Through analyzing the general geometric error analysis model of CNC machine tools with less than five axes and the method of solving precision CNC instructions, the operating principle of the CNC machine tools is studied. At the same time, we use a transformation matrix to express the relationship between the various moving bodies. The article abstracts the complex motion relationship between entities as the relationship between mathematical matrices. The experimental results show that the theoretical method proposed in this paper can increase the machining accuracy of the machine tool by more than 50%.

We use mathematical modeling methods to incorporate new elements into the computer graphics technology and visual communication design process. This method realizes the design of a computer image visual communication system. This method uses artificial vision to model and extracts local features. The micro-partial equation obtains the background reference line of the target point in the image sequence to complete the background suppression in the image spatio-temporal domain. The experimental results show that the proposed algorithm has a better tracking effect of subsequent frames of video images and higher tracking efficiency.

Based on the R language, the article designs two universal random simulation functions for the law of large numbers, LLN-mean and LLN-graph, used to calculate related variables and draw simulation graphs. At the same time, the law of large numbers is applied to children’s education. At the same time, through correlation or correlation analysis, we can find the leading internal factors and highly correlated external factors of children’s educational activities. This provides technical support for educational decision-making, educational management, and educational research. The study results found that the law of large numbers has a good test effect on the influencing factors of children’s educational activities.

Initially we applied the same data structure to grid generation, with further research, we found that the overall calculation efficiency of such a design is not high, and it is difficult to maintain. Finally, we designed different data structures based on the different characteristics of the two parts, in the grid generation, more consideration is given to flexibility and maintainability, a method to determine the flux function through the boundary of a triangular mesh is given. This method first obtains the two-dimensional Euler equations in the normal direction of the boundary of the control volume element, in the system of projection equations, the flux along the tangent to the boundary can be regarded as passive convection, therefore, the one-dimensional Riemann problem solver can be directly used to calculate the flux function passing through the boundary of the triangular control unit. This method under various flow conditions, including supersonic pipe flow and subsonic isentropic flow with strong shock waves, all have high precision and good stability.

As the geological exploration data is relatively sparse, unevenly distributed, and contains many geological faults, simple geological surface reconstruction has certain limitations. Based on the fractional differential equations, the paper establishes a subsidence prediction model in exploring geological and mineral resources. The dynamic system described by the reaction-diffusion equation can be mapped to a nonlinear cellular network through space and time discretization. At the same time, the original partial differential equations can be transformed into ordinary differential equations. Furthermore, we can use the difference method to simulate its evolutionary behavior quantitatively. The research results show that the error accuracy between the prediction results of the fractional gray theory established in this paper and the actual engineering results is higher.

Aiming at the problems of image edge blur and detail loss in most image denoising models, an image denoising model based on improved fractional calculus is proposed. Through the classification of image noise, the integer order PDE model is discussed. Based on the mathematical theory of fractional calculus, the fractional PDE model is discussed. The model is improved by combining texture detection operator, gray value detection operator, smoothing factor and fast algorithm. The simulation experiment of the model is carried out based on MATLAB simulation platform. The results show that the improved model is significantly better than other comparison models in image denoising effect, and the operation efficiency is higher.

Because civil engineering structures include stressed structural members and unstressed non-structural members, it isn’t easy to obtain the true parameters of the model when modeling. The article uses a virtual reality fuzzy random modeling to establish a steel bearing force model in civil engineering operations. We determined the relevant bearing capacity parameters based on the corrosion of steel bars in civil engineering. The research found that the numerical simulation method determined in this paper has grasped the essence of stress rate, concrete material properties, and dynamic load effect to a considerable extent.

This article uses structural equation modeling (SEM) to analyze and study the factors affecting corporate financial risks. At the same time, the regression analysis model is used for risk warning. The empirical test effectively proves that the formation of corporate financial risk is closely related to the industry environment in which it is located. After estimating the model’s parameters, it is found that monetary policy, enterprise-scale, market supply and marketing, and macroeconomic factors are the main factors that affect the financial risks of enterprises.

This article introduces the development history of fractional calculus and expounds on the positive significance of fractional calculus in integrating higher mathematics teaching. The author introduces an ordinary differential equation model case appropriately. In this way, ordinary differential equations play an important role in improving college students’ mathematical thinking ability and mathematical application ability.

This article first uses the gray correlation analysis combined with the gravitational search algorithm model to model the time series linearly. In this way, the predicted value of the GEM stock price is obtained. The simulation analysis of the calculation example found that the average relative error of the prediction result of our proposed model is 0.095 and the operation efficiency is high.

The article uses mathematical theory to derive a quasi-linear differential equation describing the law of memory forgetting in psychology. The nonlinear automatic control machine model is used to preliminary model the indiscriminate memory problem in psychology. The research obtains the recommended evaluation value with the forgetting characteristics in memory psychology. The experimental results found that the model reasonably solves the problem of quantification of timeliness.

Based on the strong classification feature recognition algorithm, the calculation algorithm of a text semantic similarity is studied with the performance evaluation in this paper. In order to achieve a general algorithm for this function, the semantic function library based on a semantic recognition code as a comparison object is designed. It drives the algorithm modules of two fuzzy neuron deep convolution machine learning, and between these two processes of machine learning, a rigid algorithm based on Fourier transform frequency domain feature is extracted. Finally, a more complex machine learning general algorithm is realized by the use of external data fuzzy algorithm and de-fuzzy algorithm before and after the algorithm module. It is also a technical innovation in this paper. Through the performance evaluation based on the subjective evaluation of volunteers, it is found that the system focuses on the text semantic similarity evaluation of the Chinese language, and achieves a comparison result of 81.78% of the artificial judgment accuracy rate, and only 5.52% of the volunteers believe that the system judgment result is completely different from that of manual judgment.

This paper studies a combination forecasting model with strong adaptability and high dimension to evaluate value of patents, and verifies the model empirically in the research. Through the AHP analysis, five necessary factors that affect the value of patents are discovered, which come from both the characteristic factors of the patent itself and the institutional characteristic factors that attempt to transform the patent. We’ve constructed a state space model through some data that can already obtain the added value of its patent through the Hejun value evaluation model and deployed the state space model in the artificial intelligence data space to have the neural network training. Another part of the known data is used to empirically verify this model, and it is found that the data fits well. Not only can the model be used for patent conversion institutions to evaluate patents, but also for patent holders to evaluate patent conversion institutions.

Because the current computer sensor data positioning analysis has positioning difficulties and false positioning problems, we use the Lagrangian multiplier method of the interactive direction to disassemble the computer sensor sound source. Through this algorithm, the information fusion of computer sensor nodes is realized. After using Lagrangian mathematical equations, these error correction measurements have achieved better target positioning results. Theoretical analysis and experimental results show that the algorithm improves the speed of computer sensor data association. To a certain extent, the correlation accuracy is improved.

First, this paper uses the Lyapunov stability function to construct the time-space implicit calculus equation model of the integrated manufacturing of single-chip microcomputers for the abnormal diffusion phenomenon. Secondly, we use the differential data fusion algorithm modeling of the discrete manufacturing system and introduce the implicit calculus equation modeling method. Finally, the article uses the singular boundary method to give the simulation results. The study found that the implicit calculus equation modeling method is simpler than the existing model, and the physical and statistical concepts are clear.

This article first adopts a fuzzy mathematical analysis model and proposes a mathematical model of fuzzy characteristics of music categories. Second, the article extracts audio data characteristics and conducts music classification experiments. The article establishes a DNN-Bottleneck feature framework, extracts robust perceptual features from audio data, and then encodes to achieve fast audio perceptual hashing. Experiments verify the effect of different feature selections on the semantic space representation of music emotions and the impact on retrieval performance.

The article uses the law of large numbers to analyze and uses the equivalence relationship on the data set to measure the degree of uncertainty of knowledge. In this way, we can analyze the relationship between the employment of graduates from colleges and universities and professional education training. The article describes several collective category models of college graduates’ employment rate and enrollment scale. This can provide an important theoretical reference for solving the actual social problems related to employment and enrollment.

The nonlinear differential equation option pricing formula is invaluable in financial derivatives investment risk assessment. This article applies the theory of nonlinear differential equations to deal with financial risks in commodity and currency markets. Through this condition, we obtain the fair price process of contingent rights under the classic Black-Scholes model and the price process of the optimal growth investment strategy. The results show that the risk measurement under stable distribution is suitable for investors to manage risk.

This article proposes an approximate high-dimensional optimization method based on a multi-layer public space design reduction strategy. At the same time, we combined the analysis of fractional differential equations to decompose the design space and improve the matrix condition number. Finally, the article proposes a new point cloud curve matching method for public space design. The experimental simulation found that the mixed-use of fractional differential equations and shape space calculations to generate models have good results.

As a basic place for human daily life, the safety performance of architectural structure in practical application directly determines the future trend of social economy and urban construction development. By understanding the relationship between the internal and external environment of the structure and using advanced theoretical knowledge to evaluate the effectiveness of the structure, we can find effective countermeasures to solve the problem. Therefore, on the basis of defining the stochastic process model of resistance, this paper uses the reliability period analysis method to compare the structural effectiveness indicators of the proposed structure and the existing structure, and thus makes clear the differences between the traditional reliability calculation method and the time period analysis method, and analyzes the particularity of different structures.

In this paper, the new energy automobile front-end frame of a factory is taken as the research object, the polypropylene plastic is used to replace the traditional sheet metal material, and the hyper mesh is used to load the front-end frame’s six loading loads, which are the locking limit tension and the cushion impact force, respectively, pedestrian impact strength, condenser support strength, radiator support strength, oil cooler support strength, ensure to achieve certain mechanical properties before production. The maximum warpage deformation is 1.023 mm by mold flow analysis with Moldflow. It does not meet the needs of manufacturers, so it is necessary to optimize the process parameters. We use the mold temperature, melt temperature, holding pressure, injection time, and holding time as test factors, and take the amount of warpage as the optimization goal. Then this paper uses the orthogonal test method to design the test plan and establishes 25 groups of 5-level 5-factor orthogonal tests. Moreover, the effect of the deformation on the warpage is analyzed. These are all to obtain the minimum warpage deformation and find the optimal combination of process parameters. Verification by numerical simulation shows that the warpage is reduced to 0.632 mm. By analyzing the range and variance, the combination of process parameters is optimized, and the warpage is effectively reduced. In the premise of satisfying mechanical properties, plastic instead of steel, to achieve a lightweight design. It provides correct theoretical guidance for setting the actual injection molding process parameters.

As the main development direction of the new era, it not only makes rational use of modern technology and information resources, but also optimizes the overall level of urban logistics planning, construction and management. Now, with the continuous improvement of residents’ living standards, it has gradually become the focus of attention. The difference between the Internet of Things and the digital city’s public information platform based on the comprehensive perception of urban information resources allows in-depth exploration and analysis, and ultimately improves the overall urban logistics construction management service level. On the basis of understanding the current scientific research results and public information management platform construction experience, starting from the construction of the current public information management platform, based on the information cloud service architecture, verify and analyze the operation of the public information management platform of the information cloud service architecture. Can lay the foundation for construction. From the perspective of logistics, this paper makes an in-depth exploration of the uncertainty of production and customer demand in public system management, and gives a mathematical model of fuzzy constrained programming combined with the characteristics of the information cloud structure to solve the detailed aspects of the system at a higher level.

An electrostatic precipitator is an essential piece of equipment to eliminate atmospheric dust pollution. Its power supply is of great significance to the working efficiency and reliability of the dust collector. This paper uses field-programmable gate array (FPGA) technology to design an electrostatic precipitator power controller. In this paper, a fuzzy control scheme with variable scale factors is adopted to make the highest average voltage between the two poles of the precipitator better approach the critical breakdown voltage. In this paper, the transfer function is derived based on the finite element differential equation and the method of three-dimensional drawing. In this way, the influence of parameters such as the coupling inductance of the pulse power supply, the coupling coefficient, and the parasitic resistance of the dust removal chamber on the load oscillation can be obtained. It is found that the control system can control the electrostatic precipitator power well. It can significantly improve dust removal efficiency.

Identity authentication and identification as the main activities in the modern human daily life, in the development of social economy and technological innovation of science and technology, information security and public security and other fields of identity recognition technology put forward higher request, not only to accurately record the relevant data information, and use of advanced technology concept advanced authentication technology is put forward. Knowing the living habits of current social residents, they need to choose appropriate ways to prove their identity, whether they enter the computer system or participate in financial services. For example, passwords, keys, ID cards and other contents are traditional means of identity authentication. As the reliability of traditional identity authentication means is getting lower and lower in today’s social network environment, in order to meet the needs of increasingly innovative network platforms and enhance the security and reliability of identity authentication technology, researchers propose to use biometric identification, among which face recognition is the most common. This recognition method is more direct and effective than palmprint, retina, fingerprint and so on, and occupies an important position in the current biometric research topic. After understanding the application of hidden Markov model (HMM) based on wavelet transform and its improved model in the field of face authentication, this paper analyzes the influence of various observation vector optimization methods on the authentication probability, and proposes a dynamic threshold method combined with the authentication model, in order to obtain a better authentication probability. The final design and implementation of the face information as the core of the identity authentication system. The improved hidden Markov model can effectively represent the correlation between face organs, so it has a positive role in the application of face modeling and authentication technology.

In the context of information construction, faced with a large number of network information data, in order to obtain more valuable information in an effective time, researchers put forward a recommendation algorithm for information explosion. Because the recommendation algorithm has been successfully applied in many fields such as business, the relevant algorithm system has also begun to be fully implemented in the field of books. There are many kinds of recommendation algorithms, among which collaborative filtering recommendation technology is the most widely used. Therefore, based on the humanized library service concept, this paper mainly studies the influencing factors of reader satisfaction, and on the basis of constructing multiple linear regression model, clarifies the practical significance of constructing collaborative filtering personalized recommendation system for libraries. Then, an improved clustering algorithm is proposed to reduce the dimensionality of the original matrix, and an empirical analysis is made on the book collaborative filtering personalized recommendation system based on linear regression equation by using the operation idea of calculating the score according to the borrowing time. The final results show that, according to the multiple linear regression model between reader satisfaction and its influencing factors, in order to improve library service quality and build a good learning and reading environment, collaborative filtering algorithm should be combined to build a personalized book recommendation system, and this system is feasible in practical application..

With the innovation and development of commercial shopping centers in China, the shopping environment is becoming more and more colorful. However, in today’s social environment, the central function of low-level consumption experience can no longer meet the needs of the masses. Therefore, in the design of indoor environment, we should start from a new perspective, focusing on the difference of internal space and the experience of consumption mode, so as to meet the development needs of commercial shopping in the future. Based on the research on the indoor environment of comprehensive commercial shopping center, comprehensive commercial shopping center in a certain area as the research target, the corresponding mathematical model was constructed, and using the measured method validation build the model of reliability and validity, thus obtains using CFD numerical simulation software of thermal and moisture environment of building an in-depth exploration, The effective countermeasures are put forward for the original air distribution mode. Comparing the improved scheme with the original scheme, it is found that the former can provide effective basis for the interior environment design of similar comprehensive commercial shopping malls.

Absolute income hypothesis, as one of the most critical contents in the employment theory proposed by Keynes, is a hypothesis proposed according to the consumption level and specific changes of consumers. In mathematics to study the core of sustainable development economics, the research of scholars on the relationship between economics and mathematical tools put forward more questions, most of the research results are based on inspection absolute income hypothesis as the core, in the present theoretical basis of economics at the same time, the use of statistics to provide practical research of the required information, select effective study method combined with mathematics. In this article, therefore, to understand the traditional research methods of mathematical statistics, on the basis of absolute income hypothesis proved for the empirical analysis, and the final result proves that the mathematical tools, has a close relationship between knowledge economics, statistics, three can analysis in the organic fusion of modern economic life, the number of specific problems existing in the practice of social and economic development, Therefore, it belongs to the main direction of economic theory exploration.

Nonlinear fractional differential equations are an important part of advanced mathematics teaching. The existence and uniqueness of its positive solution have always been a hot topic of academic discussion. This article uses differential inclusion theory and the Lyapunov stability method to analyze the finite-time stabilization control problem of the discontinuous mathematical adjustment model. The article uses a modified decomposition method and convergence acceleration technology in the application of fractional differential equations. The method gives an analytical approximate solution sequence that is easy to calculate, verify, and quickly converge. Finally, examples of Lyapunov stability and the construction of the V function can inspire students to understand ordinary differential equations and increase their interest in learning.

Campus university library as a spiritual force, in the development of social economy and science and technology innovation, according to the requirements of education management research scholars and students growth changes proposed learning Shared space, the effective integration of space, resources, service as one of the new construction idea, not only makes the university library become more perfect effective, It can also enhance the cohesion and innovation of internal operation. Nowadays, with the increase of the number of university libraries around the country, the scale of internal construction is getting bigger and bigger, and the planning and design of learning shared space based on university libraries has become the focus of scientific research. In essence, learning shared space, as a seamless learning environment, begins to innovate toward intellectualization and modernization while transforming the functional role of university libraries. In this article, therefore, learn about the current university library, on the basis of Shared space planning and design content, according to the fuzzy matrix model, analysis of the application of image retrieval algorithm is verified, the final results show that in the university library to promote learning sharing space, can not only meet the diverse needs of the readers, you can also change the traditional mode of the library service.

in the network technology increasingly innovation, weibo social media such as WeChat gradually become people thought together and important platform of communication, both theoretical knowledge and practical case studies, have proved that social media can be intuitive show people the focus of the current problems, to provide effective basis for market development and investment decisions. Especially in the comprehensive promotion of text mining technology, topic extraction related to corporate social media has been reasonably applied in the financial market. However, due to the problems of sparse and unstructured data, topic extraction in practical application has become the main subject explored by researchers and scholars. This paper studies enterprise microblogging social media, for example, using both the theme of the text content and platform interactive method, according to the relations between the two kinds of typical weibo relation and the matrix, and by using two consecutive nonnegative matrix decomposition process is analyzed, finally the corresponding distance as a result, and extracting keywords to express the relationship. The actual verification results show that the clustering accuracy and theme similarity of this method are more effective than traditional theme extraction methods in corporate social media.

Deployable antennas, as the core content of national defense technology research at this stage, have the advantages of large flexibility and light weight in practical applications, so this type of antenna can also be called a rigid-flexible hybrid structure. According to the theoretical analysis of the dynamics of flexible multi-body systems, it can be seen that effective control of unfolding antennas is a basic requirement for practical applications. Due to the instability of the specific numerical solution of the static Lagrangian function, it is difficult to completely meet the constraint equation, which is also the main factor affecting the steady development of flexible multibody dynamics. Therefore, in-depth discussion of the numerical calculation method of the static Lagrangian function, obtaining efficient and stable numerical methods from it, and providing effective information for the process control of the deployment of the antenna, is the focus of scientific research scholars at this stage. Based on the understanding of the flexible multi-body dynamics modeling method, this paper systematically analyzes the calculation method of the differential equations, and combines the direct modification method of the constraint violation of the augmentation method to propose the simulation calculation of the model. The final results prove that the dynamics of flexible multi-body systems have a positive effect on the application analysis of deployable antennas.

In the field of computer vision development, the core problem is how to obtain high-level semantic information from the lowest level of original video data, and make a correct understanding. At present, the research topics proposed at home and abroad are mainly focused on the visual analysis of moving objects. Especially for image research in automobile field, visual analysis of moving objects is one of the most common topics. Its focus is to use computer vision technology to detect moving objects, and describe and understand them after tracking and recognizing relevant user portraits and behaviors. In this paper, taking vehicle driving posture preference as an example, linear dimension parameters were used instead of human joint Angle parameters to simply present the driving posture of vehicle users, and corresponding dimension parameters were obtained to present the driving posture characteristics of vehicle users. By inviting 50 drivers to participate in the test of driving attitude preference, cluster analysis was carried out on three sample data representing upper body attitude, and the clustering results were presented by combining with three-dimensional images. The final results show that the k-means clustering model can eliminate the influence of body size difference, accurately distinguish the preference characteristics of driving posture, and scientifically design steering wheel and car seat according to the measurement data of target users.

The phenomenon of plagiarism in coursework is common among college students. This phenomenon seriously affects the quality of higher education. The school has developed a series of homework similarity checking models to ensure the originality of English teaching coursework. The fractional differential equation method is used to classify and analyze the assignments with plagiarism suspicion. The article calculates program similarity’s fractional differential equation calculation by sequence matching algorithm in English homework. Finally, we extract AST features of similar program parts and generate spatial vectors. The research aims to find out plagiarized assignment texts by cluster analysis. Experimental research shows that the establishment of this model can assist English teachers in checking online homework. At the same time, the model can also help improve the efficiency of teachers’ homework checking.

Based on the theory of ordinary differential equations, this paper proposes a stable and discriminative method for piano tone tuning. We perform discriminative training on the hidden Markov tone model according to ordinary differential equations’ feature extraction parameters and model parameters. The model can improve the recognition rate of piano tones. This paper trains and tests the MAPS universal dataset for musical transcription of automatic piano tones. The model is uniformly trained on the synthetic part and tested on the real recording part. The experimental study found that the proposed model has high recognition stability and accuracy in piano tone recognition.

After the input signal of e-commerce network information enters the network, it will inevitably be polluted by network delay. There is an error between the network output signal obtained by the receiver and the input signal of the transmitter. We combine control combination algorithms with mathematical models. And the power spectral density function is introduced into the signal transmission mathematical model of the e-commerce platform. Experiments prove that the new model is closer to the transmission efficiency change of the actual network communication signal than the traditional model.

This paper discusses a class of inhomogeneous fractional differential equations with boundary conditions. At the same time, we apply it to the database network encryption model. In this paper, the fractional differential equation algorithm segments the big data in the cloud environment, and the homomorphic algorithm is used for encryption. We encrypt the algorithms and store them in the database, respectively. When the model is queried, the corresponding ciphertext data in the database can be matched according to the type of query statement. The experimental simulation realizes the information retrieval and statistics in the case of full ciphertext on the server-side.

Basketball is one of the sports that people love. This paper uses fractional differential equations to perform shot visual proofreading. At the same time, we propose a visual proofreading method for the optimal shooting angle. We extract the features of the shooting trajectory according to the distribution of corner points and edge contours of the trajectory image. So far, the automatic capture method of basketball shooting trajectory based on the fractional differential equation is completed. We found that the algorithm in this paper greatly improves the player’s shooting technique through experimental simulation research.

Vocational education and dynamic social development are two complex nonlinear systems. Establishing the linear system theory of vocational education in university education is a relatively complex subject. We use qualitative and quantitative methods to establish nonlinear differential equations of college students’ vocational education. This paper analyzes the structural characteristics of the vocational education industry-education integration system and the dynamic factors that cause the evolution of the nonlinear system. Finally, the article verifies the higher vocational education system’s non-equilibrium, openness, and nonlinearity through examples.

This paper establishes a three-dimensional virtual landscape model based on statistical equations. This paper completes the analysis of interior design requirements by analyzing the structure of the interior design platform and the indoor positioning algorithm from the three-dimensional virtual perspective. We realize the 3D reconstruction of indoor landscape through the 3D visual image reconstruction module and VRLM browser module. The experimental results show that the designed 3D virtual landscape is more realistic. Its artistic effect is better.

Under the background of the marketization of agricultural products, the lack of farmers’ risk analysis mechanism has resulted in a structural imbalance between the supply and demand of funds in rural areas. The increase of the rural economy is significant to social development and stability. Then the article uses the ordered Probit model to carry out statistical regression analysis on the rural economic samples. The study found that the lack of supply institutions, the incompatibility of loan supply and demand, and the single type of insurance caused the development of the rural economy to be limited.

This paper introduces a method for dynamic loading of human-vehicle powertrains during dangerous driving. At the same time, this paper establishes a performance evaluation index of the human-vehicle (electric vehicle) powertrain system based on the second derivative functional. We have analyzed and established the calculation formula of the excitation force of the electric vehicle drive train in unstable driving conditions. We use the numerical solution method to perform the dynamic model simulation calculation on MATLAB. The study found that the high-frequency excitation force increases the amplitude of the acceleration power spectrum of the electric vehicle system. At the same time, the research results prove that the state-space model of the electric vehicle vibration system and the selected parameter values are effective.

This paper proposes a denoising algorithm for physical, electronic images based on fractional differential equations. The algorithm effectively combines fractional calculus theory and gradient descent flow. At the same time, we introduce the time factor into the improved denoising model based on the spatial fractional partial differential equation. We take advantage of the unique amplitude-frequency characteristic of fractional differential operation to preserve the texture details with little grayscale change in the smooth area of the image. The model realizes the simultaneous denoising of physical, electronic images in the time direction and the spaceplane. The experimental results show that the fractional-order partial differential equation method has more advantages than the integer-order partial differential equation in denoising and reducing the staircase effect.

The electronic information security model has the characteristics of nonlinearity and uncertainty. There will be great limitations if we use traditional mathematical theory for processing. Therefore, the paper proposes an electronic circuit information security simulation method utilizing nonlinear differential equations. The method uses a fractional reactance approximation circuit to build a nonlinear differential operator. The model modifies the circuit impedance function in electronic information security to form a transfer function. Then with the help of this function, we build the block diagram of nonlinear differential equation simulation. Experimental research shows that the algorithm proposed in this paper is simple, and the amount of data is small. At the same time, the experiment also verifies the correctness and effectiveness of the processing method.