Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system

MVC is a framework mode that compulsorily separates the input, processing and output of the application. Using MVC applications is divided into three core components: model, view and controller, each of which handles its own tasks.

M refers to the data model. It is the core of the MVC design pattern. It encapsulates the core process and business rules of the system. It is the internal abstraction of the problem logic handled by the software independent of the external display content and form. It is independent of the concrete Express and I/O operations. V refers to the user interface, which is the interface that the user sees and interacts with. It is mainly responsible for displaying relevant data to the user and can accept the user's input data, but it does not perform any actual business processing. It obtains the display information from the model, and there can be multiple different display forms or views for the same information. C is the controller. The controller defines the behaviour of the application, interprets user actions, is responsible for the synchronisation between the model and the view, accepts user input and calls the model and view to complete the user's request. Usually, a view has a controller. The purpose of using MVC is to separate the implementation codes of M and V so that the same program can use different manifestations. The purpose of C is to ensure the synchronisation of M and V. Once M changes, V should be updated synchronously. Figure 1 shows the respective functions of the three modules and the relationship between them [1].

Fig. 1

For the development of Web applications, it is not easy to design and develop a reliable and stable framework from scratch. With the maturity of Web development technology, there are some ready-made excellent frameworks in the field of Web development, and developers can use them directly. The front-end development of this system uses the Struts framework, the data mapping uses the Hibernate framework and the Spring framework is used to ensure the integrity of the data.

The Struts framework is a typical framework based on the MVC mode application architecture. Struts provides implementation components for these three classes. The implementation components used by the system for these three classes are Java-a Bean, Java Server Pages (JSP), Servlet and the Struts framework structure is as follows as shown in Figure 2. The Struts technology is mainly used on the M (presentation layer) of the MVC mode. The processing flow of the Struts framework clearly reflects the advantages of the MVC mode. The biggest feature of using Struts technology to design the presentation layer is to put a lot of logic in the configuration file instead of the program, so as to avoid the need to change the program when business needs change in the future.

Fig. 2

Hibernate is a full-featured, open-source OR mapping framework on the Java platform. It is an object/relational database (Object/Relational Mapping [ORM]) mapping tool oriented to the Java environment. It not only manages the mapping of Java classes to database tables (including the mapping of Java data types to SQL data types) but also provides data query and retrieval the data method can greatly reduce the time of manually using SQL and JDBC to process data during development. Compared with using JDBC and SQL to manually operate the database, using Hibernate can greatly reduce the workload of operating the database [2].

Fig. 3

As shown in Figure 3, it is the Hibernate framework structure. The application program has a relationship with the database through Hibernate and operates on the data. Hibernate itself maps classes to rows in the database through properties and the class mapping file (mapping.xml). Thus, applications can directly access the database through persistent object classes, instead of having to use JDBC and SQL for data operations.

The Spring framework provides a full-featured MVC module for building Web applications. Using Spring's pluggable MVC architecture, you can choose to use the built-in Spring Web framework or a Web framework such as Struts. Through the strategy interface, the Spring framework is highly configurable and contains a variety of view technologies, such as JSP technology, Velocity, Tiles, item and POI. Spring separates the roles of the controller, model object, dispatcher, and handler object. This separation makes them easier to customise. The Spring frame structure is shown in Figure 4.

Fig. 4

Fig. 5

SSH is an integrated framework of Struts+Sprint+Hibernate and is currently a popular open-source framework for Web applications. Among them, using Struts as the overall system infrastructure, responsible for the separation of MVC, in the model part of the Struts framework, the Hibernate framework is used to provide support for the persistence layer, and the business layer is supported by Spring. Each layer has clear functional responsibilities and should not be mixed with other layers. Each layer is connected with the other through communication interfaces. The three-tier SSH architecture system is shown in Figure 5.

The data collector in the system hardware is composed of chips CP2210 and C8147 single-chip microcomputer, which realises network big data collection and transmits the collected data to the network processor through the network interface. The hardware structure diagram of the data collector is shown in Figure 6.

Fig. 6

It can be seen from Figure 6 that the data collector power supply sends out a 6 V voltage, which is transmitted to the microcontroller voltage regulator through the REGIN pin of the microcontroller, adjusts the voltage to the 4 V voltage required for the microcontroller to work and passes the remaining 2 V voltage through the VDD pin to send it to other parts for use. The one-chip computer exchanges information through P3, P4 and other I/O pins. The signal obtained from the network passes through the signal adjuster and reaches the A/D converter from the P25 pin of the single-chip microcomputer. The A/D converter converts the signal into corresponding data, thereby completing the network data collection.

The storage module is the core of the big data classification system and is used to store all the data in the system. Before constructing the storage module, it is necessary to clarify the system requirements, and then map tasks to different types of analysis models and mining models through the semantic layer, and use the data in the system to obtain the final solution. Based on the hierarchical model method and the group collaborative intelligent clustering hierarchical model, this paper divides the storage modules of the big data classification system into the application layer, functional layer, semantic layer, design layer and data layer. The specific structure is shown in Figure 7.

In Figure 7, the application layer is the top layer of the storage module of the big data classification system, which can describe, distinguish and assign tasks; the function layer is the support structure of the application layer, including related function codes, and the function layer is the big data in the data. The storage module is a bridge for interaction with users; the semantic layer realises the transformation from the data model of the design layer to the business of the functional layer and converts the data model of the design layer into business terms for description; the design layer uses the information package diagram to set classification based on system requirements. Content visually describes the classification of data through the data model and respond to the retrieval needs of users of the big data classification system in real time; the data layer organises the big data through system control events, accesses the source data of the system to complete the extraction and integration of the source data and other operations, and its storage is designed as a relational database structure for the query [3].

Fig. 7

In order to achieve big data classification, the system software uses differential equations for data classification processing and establishes a second-order delay differential equation in the Bochner-Riesz space: (1) x˙(u)=Bx(u)+Cx(u−e(u)) \dot x(u) = Bx(u) + Cx(u - e(u)) In Eq. 1, e(u) is the time delay term in the stable state x(u) of the characteristic solution of the second-order delay differential equation; B and C are the parameters of the second-order delay differential equation. The eigenvector of the second-order delay differential equation at the boundary stable equilibrium point eQ_i(u)/(eu) = U_i(u)Q_UQi + L_i(u)Q_LQi is expressed as: (2) φ1(e1(u))=φ+e1(u)Q(X1+X2+X3)−1QU+(u1−e1(u))[QX1−1QU+L(X2+X3)−1LU] {\varphi _1}({e_1}(u)) = \varphi + {e_1}(u)Q{({X_1} + {X_2} + {X_3})^{ - 1}}{Q^U} + ({u_1} - {e_1}(u))\left[ {QX_1^{ - 1}{Q^U} + L{{({X_2} + {X_3})}^{ - 1}}{L^U}} \right] In Eq. 2, L_i(u) and U_i(u) are used to describe the stable state of the parameter u at the lowest point and the highest point of the boundary, respectively; Q_LQi and Q_UQi represent the lowest and highest equilibrium points of the boundary, respectively; Eφ represents the eigenvector of the characteristic solution of the second-order delay differential equation [4].

Perform Lyapunov functional processing on the stable solution of the second-order delay differential equation at point F. According to the optimisation theory, a new geometric region is obtained. By constructing an appropriate Lyapunov functional and adding the auxiliary integral matrix, the second-order delay differential is obtained the stable solution of the equation is: (3) v1=[v11Uv13Q10000v22Uv24Q20000v33Uv35Q30000v44Uv46Q4] {v_1} = \left[ {\matrix{ {{v_{11}}} & {U{v_{13}}} & {{Q_1}} & 0 & 0 & 0 \cr 0 & {{v_{22}}} & {U{v_{24}}} & {{Q_2}} & 0 & 0 \cr 0 & 0 & {{v_{33}}} & {U{v_{35}}} & {{Q_3}} & 0 \cr 0 & 0 & 0 & {{v_{44}}} & {U{v_{46}}} & {{Q_4}} \cr } } \right] (4) v1=[Q5000v55Uv57Uv68Q6000v66] {v_1} = \left[ {\matrix{ {{Q_5}} & 0 & 0 & 0 & {{v_{55}}} & {U{v_{57}}} \cr {U{v_{68}}} & {{Q_6}} & 0 & 0 & 0 & {{v_{66}}} \cr } } \right] Under the stability constraint of the double limit condition, taking the solution vector of the region M (0) adjacent to the origin as the initial condition, the parameters for the existence of stable solutions of the second-order delay differential equation are: (5) vn=[Vn+11Qn+11000]U {v_n} = {\left[ {{V_{n + 11}}{Q_{n + 11}}000} \right]^U} In the formula, it is the same as the average characteristic functional of ν1. According to the periodic independent wave solution of the second-order delay differential term, the stable solution vector is used as the clustering centre vector of big data classification to construct the mathematical model of differential classification.

Based on the MVC model SSH framework, the child mental health information tracking system is based on the actual and specific conditions of our school's mental health education, comprehensively using modern information technology to reshape and recreate the child's mental health information, aiming to provide psychological counselling through Internet technology. The teachers can get timely and comprehensive information about children's various situations and trends. Compared with traditional infant mental health education, it truly reflects the superiority of modern IT technology in infant mental health education. At present, there is not much research on the application of mental health information to network tracking. In order to facilitate the future upgrade of the system, this system adopts the lightweight J2EE software framework of Struts2 + Sprint + Hibernate and the efficient and intelligent SQL Server 2008 database technology for development. The system has good scalability, reusability, portability and maintainability [5].