Problem-based Learning Combining Seminar Teaching Method for the Practice of Mathematical Modeling Course's Teaching Reform for Computer Discipline

Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.

Mathematical model of wave transformation over radial sand ridge field on continental shelf of South Yellow Sea

According to a deformed mild-slope equation derived by Guang-wen Hong and an enhanced numerical method, a wave refraction-diffraction nonlinear mathematical model that takes tidal level change and the high-order bathymetry factor into account has been developed. The deformed mild-slope equation is used to eliminate the restriction of wave length on calculation steps. Using the hard disk to record data during the calculation process, the enhanced numerical method can save computer memory space to a certain extent, so that a large-scale sea area can be calculated with high-resolution grids. This model was applied to wave field integral calculation over a radial sand ridge field in the South Yellow Sea. The results demonstrate some features of the wave field： （1） the wave-height contour lines are arc-shaped near the shore; （2） waves break many times when they propagate toward the shore; （3） wave field characteristics on the northern and southern sides of Huangshayang are different; and （4） the characteristics of wave distribution match the terrain features. The application of this model in the region of the radial sand ridge field suggests that it is a feasible way to analyze wave refraction-diffraction effects under natural sea conditions.

Mathematical model analysis of new-type magnetic integrated CRT considering magnetic leakage

A novel magnetic integrated controllable reactor of transformer type(CRT)has the advantages of simple structure,flexible assembly,convenient maintenance and practicability.To analyze its operation characteristics accurately,we establish corresponding equivalent mathematical model considering magnetic leakage based on magnetic circuit and circuit dualistic transformation method.The distribution of magnetic leakage field of each winding is analyzed qualitatively,and the analytical calculation formulas of magnetizing inductance and leakage inductance of each winding are derived.Based on this,the analytical calculation formulas of short-circuit impedance and winding current of CRT under different working conditions are derived.The field-circuit coupling finite element model of the magnetic integrated CRT is established to simulate the current of each winding under different working conditions.The results show that the analytical calculation results of each winding current have good consistency with the finite element calculation results,indicating the validity of CRT equivalent mathematical model and correctness of the analytical formulas of leakage inductance,short-circuit impedance and winding current of CRT.The working winding current of CRT is increasing gradually with the operation of control winding in turn to realise the transition of CRT compensation capacity from zero to a rated value.

New Mathematical Model Based on Affine ransformation for Remote Sensing Image with High Resolution

This paper calculates the parameters of image position and orientation,proposes a mathematical model and adopts a new method with three steps of transformations based on parallel ray projection.Every step of the model is strict,and the map function of each transformation is the first order polynomials and other simple function.The final calculation of the parameters is for the linear equations with good status.As a result,the problem of the relativity of image parameter calculation is solved completely.Some experiments are carried out.

Mathematical, Mathematics Educational, and Educational Values in Mathematical Modeling Tasks

Purpose:The purpose of this study is to explore the mathematical values,mathematics educational values,and educational values invoIved in mathematical modeling tasks based on different mathematical modeling perspectives.Design/Approach/Methods:In this con text,the prese nt study is a qualitative research based on document analysis.The data were analyzed usingsemantic content analysis,and the selected modeling tasks based on different mathematical modeling perspectives were examined at the sentence level.Findings:Control,mystery,and openness mathematical values appeared in all mathematical modeling tasks,and rationalism and objectivism mathematical values appeared in realistic/applied and socio-critical modeli ng perspectives.Product,exploration,creating,releva nee,pleasure,and application mathematics educational values also emerged in all modeling tasks.Educational values of social justice,equity,social welfare,humanity,and altruism were more important in the socio critical modeling,while the value of individualism was more emphasized in the model-eliciting approach.Originality/Value:By determining mathematical,mathematics educational,and educational values involved in mathematical modeling tasks based on different mathematical modeling perspectives,an effective and more value-balaneed mathematical modeling instruction can be provided.

Theoretical research and practical application of Mathematical economic models

Mathematical economic modeling is widely used to provide a reference for policy makers and guidance for the specific work of many departments, such as saving expenditures, reducing costs and improving profit. Particularly, it can predict and estimate the future, playing a great role in promoting the rapid development of science and technology as well as the management of market economy. In general, mathematics does not directly deal with the objective conditions on the management of market economy. In order to use mathematics to solve problems in the field of the management of market economic, it is necessary to carry out mathematical economic modeling.

ANALYSIS SOLUTION OF ONE-DIMENSIONAL MATHEMATICAL MODEL ABOUT HEAVY METAL TRANSPORT FOR RIVER WATER

Water quality model about heavy metal under general initial and boundary conditions was studied. The model includes adsorption of suspended sediment, adsorption of bed load, advective diffusion of flow water, which affect the concentration of heavy metal in river water. Laplace transforms method was adopted, its integral equation of the concentration of diluting heavy metal and solid heavy metal was given. The characteristic of the model under constant solution was discussed. Using this model the prediction of mercury (Hg) ions concentration distribution along a section of Yellow River in Lanzhou, China was performed. The computational value is approximately equal to the measured value.

Analytical solution to one-dimensional mathematical model of flow and morphological evolution in open channels

The evolution of open-channel flow and morphology can be simulated by one-dimensional(1D) mathematical models. These models are typically solved by numerical or analytical methods. Because the behavior of variables can be explained by explicit mathematical determinations,compared to numerical solutions,analytical solutions provide fundamental and physical insights into flow and sediment transport mechanisms. The singular perturbation technique derives a hierarchical equation of waves and describes the evolutionary nature of disturbances in hyperbolic systems. The wave hierarchy consists of dynamic,diffusion,and kinetic waves. These three types of waves interact with each other in the process of propagation. Moreover,the Laplace transform is implemented to transform partial differential equations into ordinary differential equations. Analytical expressions in the wave front are subtracted by the approximation of kinetic and diffusion models. Moreover,an analytical solution consists of a linear combination of the kinetic wave front and the diffusion wave front expressions,pursuing to describe the physical mechanism of motion in open channels as completely as possible. Analytical solutions are presented as a combination of exponential functions,hyperbolic functions,and infinite series. The obtained analytical solution was further applied to the simulation of flood path and morphological evolution in the Lower Yellow River. The phenomenon of increased peak discharge in the downstream reach was successfully simulated. It was encouraging that the results were in good agreement with the observed data.

Neural Networks and the Study of Time Series： An Application in Engineering Education

Time series are an important object of study in sciences, engineering and business, especially in cases where it is expected to know, predict and optimize behaviors. In this context, we intend to show the feasibility of using artificial neural networks in the study of several time series in an engineering course, especially those that have no overt behavior or are not able to be modeled mathematically in a simple way and have direct application in the education of future engineers.

Semantic model and optimization of creative processes at mathematical knowledge formation

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

Applications of optimal mathematic-physical models in metallurgical manufacture scheduling system at Baosteel

The transfer of mass flow between ironmaking and steelmaking process atBaoshan Iron and Steel Co. Ltd. has been analyzed. The mathematic-physical models of transportscheduling for hot metal manufacturing have been researched combined with the practical problem inthe metallurgical manufacture procedure. Taking into account these models, the scheduling softwarehas been designed, programmed and tested on-line. The new automation system of production schedulinghas been implemented successfully at Baosteel, which produces a great economic benefit.

Research on Yield and Quality of Hybrid Rice under Efficient Application Amount of Phosphorus and Potassium

[Objective] Application of P and K was not reasonable in southwest rice producing area, with no effective method for guiding application of P and K. This study aimed to conduct experiments with the same N application and different P and K application in different ecological points, to explore a scientific and efficient management method of P and K nutrients and provide guidance for application of P and K in rice production. [Method] Hybrid rice Chuanxiang9838 was used as experimental material to study the relationship among application amount of P and K, utilization rates of P and K, rice yield and rice quality in seven ecological points of four provinces （municipalities） including Sichuan, Chongqing, Yunnan and Guizhou. The application amount per hectare of P was 37.5, 75, 112.5 and 150 kg, respectively; the application amount per hectare of K was 45, 135 and 180 kg, respectively. A total of 10 treatments were set for split-plot design with three replications. [Result] Yield of Chuanxiang9838 significantly varied in different experimental locations and under different levels of P and K, interaction of ecological point and different P and K treatments varied significantly. Yield had reached the maximum in ecological point of Yunnan Binchuan and in treatment with application of N 150 kg P 75 kg K 90 kg. Efficient utilization rates of P and K varied in each ecological point, efficient application amount of P and K in Sichuan Dongpo, Sichuan Luxian, Guizhou Xiaohe and Chongqing Yongchuan was the same, while that in Sichuan Guanghan, Sichuan Zhongjiang and Yunnan Binchuan was different. The main objective of high-yield rice production was to increase the number of effective panicles per hectare and seed setting rate. Rice quality was clustered into 2 categories by locations and 6 categories by treatments. [Conclusion] Prediction models of efficient application of P and K in rice production were established, which provided guidance for high-yield rice production and rational and efficient utilization of P and K in southwest rice area.

A simulation analysis of the migration and transformation of pollutants contained in landfill leachate

A dynamic composite model for a soil-water system that can be used to simulate the movement of leachate from a landfill. The composite model includes nine sub-models that trace water movement and the migration and transformation of five pollutants(organic N, NH - 4, NO - 3, NO - 2, and Cl -) in saturated and unsaturated soil. The model to simulate the movement of leachate from a landfill in Laogang Town, Shanghai City was used. In this application, the values for the model parameters were obtained by performing a laboratory simulation experiment of water movement and pollutant migration and transformation in soil columns. Soil and leachate obtained from the landfill site and its vicinity were used in the laboratory experiments. The model was then used to simulate leachate movement and pollutant activity during the ten-year period when the landfill was in operation and in the twenty-year period following its closure. The simulation results revealed that the leachate migrated into the groundwater at the rate of 90—100 meters per year. This model can be applied in the design of future landfills in China for the purpose of assessing and forecasting leachate plumes.

Theoretical Model and Random Simulation for Nonlinear Interaction of Irregular Waves with Vertical Wall

According to the theoretical solutions for the nonlinear three-dimensional gravity surface waves and their interactions with vertical wall previously proposed by the lead author, in this paper an exact second-order random model of the unified wave motion process for nonlinear irregular waves and their interactions with vertical wall in uniform current is formulated, the corresponding theoretical nonlinear spectrum is derived, and the digital simulation model suitable to the use of the FFT (Fast Fourier Transform) algorithm is also given. Simulations of wave surface, wave pressure, total wave pressure and its moment are performed. The probability properties and statistical characteristics of these realizations are tested, which include the verifications of normality for linear process and of non-normality for nonlinear process; the consistencies of the theoretical spectra with simulated ones; the probability properties of apparent characteristics, such as amplitudes, periods, and extremes (maximum and minimum, positive and negative extremes). The statistical analysis and comparisons demonstrate that the proposed theoretical and computing models are realistic and effective, and estimated spectra are in good agreement with the theoretical ones, and the probability properties of the simulated waves are similar to those of the sea waves. At the same time, the simulating computation can be completed rapidly and easily.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

Application of Computational Fluid Dynamics to analysis of metallurgical process for continuous casting tundishes

A series of simulations by mathematical and physical modeling on fluid flow,mass and heat transfer in continuous casting tundishes have been carried out. It was found bycomputational fluid dynamics (CFD) simulation that in most cases tundish flow must be treated as anon-isothermal reactor due to the existence of temperature difference between the transport ladleand the tundish. The critical conditions when the non-isothermal flow in the tundish can not beneglected have been found by CFD simulation and water modeling. A direct measurement in a 40 ttundish has confirmed the simulation results.

Modeling and Control of the Modular Multilevel Converter (MMC) based Solid State Transformer (SST) with Magnetic Integration

Solid state transformer(SST)can provide more advanced functionalities compared with conventional transformer,and has great potential in smart grid application.Recently,the SST with medium frequency(MF)isolation link and magnetic integration feature has been proposed,which can reduce the system volume and thus increase the power density.However,the magnetic integration also introduces strong coupling between the line frequency(LF)and MF variables,which poses a great challenge on modeling and control issues.This paper proposes a modeling and control method for an SST with magnetic integration and mixed-frequency modulation.A mathematical model based on dual d-q references is deduced,and then a cascaded control system is designed according to the model.Parameters of the controller for the variables at one frequency are properly designed to avoid disturbance from the variables at the other frequency.The simulation and experimental results show good decoupling effect and satisfactory dynamics performance of the proposed control system.

Modeling and Simulation of Nine-Phase Permanent Magnet Synchronous Motor

To study the operation characteristics of the nine-phase PMSM(Permanent Magnet Synchronous Motor),this paper derived the Clarke transformation matrix of the nine-phase PMSM with the winding 3Y shifted by 20°via analyzing the harmonic subspace of the multi-phase PMSM,and further obtained its mathematical model under the rotating coordinate system.Then,a nine-phase PMSM based on the proposed model was built in SIMULINK and the operation mode of starting,braking and phase missing is simulated.The simulation results show that the nine-phase PMSM has good dynamic performance and steady-state performance,which also verifies the correctness and rationality of the motor model.

A Research and Design on Application of Genetic Algorithm

Traditional algorithms of intelligent test paper generation have some shortcomings of slow generating speed, low success probability and poor generating quality. Genetic Algorithm is a random optimization-searching algorithm based on probability. In this paper, based on the user＇ s request of intelligent test paper generation, we establish the mathematical model and object function, and give some improvements in Simple GA for test paper generation. Based on the algorithm, a automatic generating test paper system is designed and implemented.

Research and Application Prospect of Computer Simulation on Heat Treatment Process

In this paper, a modified temperature-phase transformation-stress/strain field coupled 3D non-linear mathematical model was used in the computer simulation on heat treatment processes of workpieces including catch jaw, anchor ring, cold roller, large-scale bearing roller, nitriding crank shaft, etc. The simulation on complicated technologies such as pre-cooled quenching, double media quenching, self-tempering, difference temperature heating, nitriding distortion was carried out. The optimum design of heat treatment technology has been realized. The successful application of computer simulation on heat treatment have also been demonstrated.