Teaching Reform and Practice of “Mathematical Analysis” under the New Engineering Education Paradigm

With the advent and promotion of the new engineering education paradigm,university mathematics courses face new challenges and opportunities.As a fundamental course for engineering majors,the reform of“Mathematical Analysis”is particularly crucial.This paper explores the necessity,specific practices,and outcomes of teaching reform in“Mathematical Analysis”within the context of the new engineering education.By reforming teaching content,methods,and assessment approaches,this study aims to enhance students’mathematical literacy and comprehensive abilities to meet the demands of the new engineering education development.

Simplified Modeling and Mathematical Analysis in Cardiac Electric Field Propagation for Human and Animals

The different characteristics of cardiac electric field(CEF)radiation in humans and other animals are presented in this paper.Physical modeling and mathematical analysis are developed to comprehensively unveil the properties of CEF,based on typical heartbeat waveforms.Our numerical simulation results demonstrate that the frequency bandwidths and the cycle durations of CEF are different for healthy humans versus humans on the verge of death and for humans versus other animals.The results indicate that the present study may extensively contribute towards recognizing human beings or other animal targets quickly and accurately with CEF in dangerous situations or in other applications.

Modeling Thermal Regulation in Thin Vascular Systems:A Mathematical Analysis

Mimicking vascular systems in living beings,designers have realized microvascular composites to achieve thermal regulation and other functionalities,such as electromagnetic modulation,sensing,and healing.Such material systems avail circulating fluids through embedded vasculatures to accomplish the mentioned functionalities that benefit various aerospace,military,and civilian applications.Although heat transfer is a mature field,control of thermal characteristics in synthetic microvascular systems via circulating fluids is new,and a theoretical underpinning is lacking.What will benefit designers are predictive mathematical models and an in-depth qualitative understanding of vascular-based active cooling/heating.So,the central focus of this paper is to address the remarked knowledge gap.First,we present a reduced-order model with broad applicability,allowing the inlet temperature to differ from the ambient temperature.Second,we apply mathematical analysis tools to this reduced-order model and reveal many heat transfer properties of fluid-sequestered vascular systems.We derive point-wise properties(minimum,maximum,and comparison principles)and global properties(e.g.,bounds on performance metrics such as the mean surface temperature and thermal efficiency).These newfound results deepen our understanding of active cooling/heating and propel the perfecting of thermal regulation systems.

Numerical analysis on the influence of vortex motion in a reverse Stairmand cyclone separator by using LES model

This study aims to analyze the influence of vortex motion in a reverse Stairmand cyclone separator by using LES model.The mathematical analysis indicated that the energy dissipation and the flow characteristics of incompressible fluid are directly related to on the vortex motion.The results of the Q criterion-based iso-vortex surface could well reflect the tendency of the vortex structure,in which the iso-vortex surface exhibited a distorted distribution rather than around the center axis.At the turning point of velocity vector,vortices were formed and developed,and the point was the center of the local vortex core.In addition,the vortex formed an irregular annular region around the wall at the bottom of vortex finder.The vortex structure near the dust hopper presented a strong distortion.Moreover,there were two rotating flow in the opposite direction within the dust hopper.These phenomena would affect the separation performance,which was significance to cyclone separator.

An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology

The improvements of high-throughput experimental devices such as microarray and mass spectrometry have allowed an effective acquisition of biological comprehensive data which include genome, transcriptome, proteome, and metabolome (multi-layered omics data). In Systems Biology, we try to elucidate various dynamical characteristics of biological functions with applying the omics data to detailed mathematical model based on the central dogma. However, such mathematical models possess multi-time-scale properties which are often accompanied by time-scale differences seen among biological layers. The differences cause time stiff problem, and have a grave influence on numerical calculation stability. In the present conventional method, the time stiff problem remained because the calculation of all layers was implemented by adaptive time step sizes of the smallest time-scale layer to ensure stability and maintain calculation accuracy. In this paper, we designed and developed an effective numerical calculation method to improve the time stiff problem. This method consisted of ahead, backward, and cumulative algorithms. Both ahead and cumulative algorithms enhanced calculation efficiency of numerical calculations via adjustments of step sizes of each layer, and reduced the number of numerical calculations required for multi-time-scale models with the time stiff problem. Backward algorithm ensured calculation accuracy in the multi-time-scale models. In case studies which were focused on three layers system with 60 times difference in time-scale order in between layers, a proposed method had almost the same calculation accuracy compared with the conventional method in spite of a reduction of the total amount of the number of numerical calculations. Accordingly, the proposed method is useful in a numerical analysis of multi-time-scale models with time stiff problem.

The Impact of Peer Instruction on Students’ Achievement in Mathematics Analysis

In this research,we investigated the effect of peer instruction method on the first course mathematics education students’academic achievement and the attitudes of students by using peer instruction method.The implementation was carried out seven weeks with 60 participants in an introduction to mathematics analysis lesson in Suleyman Demirel University in Kazakhstan.Two first course groups were randomly assigned to treatment and control groups.The final results were obtained to measure students’academic achievement and questionnaires used to indicate attitudes towards peer instruction.Data were analyzed,using analysis of t-test(p=0.029)with an alpha significance level of 0.05.The results of final questions indicated,peer instruction has a significant positive effect on students’achievement in the introduction to mathematics analysis course and the results of questionnaires demonstrated peer instruction(PI)has a positive impact on peers’understanding by making learning interesting and interactive,and it also creates conducive atmosphere in the class.

Optimization of Extraction Process of Polyphenols from Chrysanthemum morifolium and the Development of Chrysanthemum Rice Wine

[Objectives]This study was conducted to provide a theoretical basis for the extraction and comprehensive utilization of functional active components of Chrysanthemum morifolium polyphenols.[Methods]With C.morifolium as a raw material,polyphenols were extracted by water extraction.The extraction process of polyphenols were optimized by single factor tests on solid-liquid ratio,extracting time and times.Old rice wine selected as the base wine was added with C.morifolium polyphenol extract,honey,citric acid and other auxiliary materials to prepare a kind of chrysanthemum old rice wine.Through sensory analysis combined with fuzzy mathematics comprehensive evaluation method,the optimal formula of chrysanthemum old rice wine was determined,and the corresponding physicochemical indicators of the obtained chrysanthemum old rice wine were tested.[Results]The optimal soaking process for C.morifolium was as follows:extraction time of 20 min,a solid-liquid ratio of C.morifolium to warm water at 1:40,extraction times of 3 times.The physical and chemical indicators of the chrysanthemum wine obtained from the above optimal formula were as follows:sugar content 5%,ethanol content 11%,and pH value 4.04.The chrysanthemum old rice wine obtained was clear and transparent,and the fragrance of chrysanthemum was coordinated with the mellow aroma of rice wine.The taste was refreshing and suitable for the vast majority of people to drink.[Conclusions]The new type of chrysanthemum old rice wine combines the polyphenolic active substances in C.morifolium with the low ethanol content of old rice wine,which not only improves the utilization rate of C.morifolium,but also strengthens the health function of old rice wine products,improves the quality of old rice wine,and promotes the healthy and rapid development of the old rice wine industry.

Research on Behavior of Corrugated Packing in Vacuum Distillation Tower

The corrugated packing is prone to break down easily, which can affect the tower efficiency substantially. It is the inner environment of the vacuum distillation tower including the temperature and chemical nature of fluid that lead to the packing damage. The theoretical analysis indicates that it is the inner material flow of vacuum distillation tower that leads to the vibration of packing, which can affect the corrosion fatigue of packing significantly. Meanwhile, the modal shape and inherent frequency of packing under prestress can be obtained by means of mathematical analysis. Based on the two kinds of analysis, the flow induced vibration and corrosion fatigue are accountable for the failure of packing.

Formula Optimization of Wheat Germ Solid Beverage

[Objectives]This study was conducted to develop a health-care product with smooth taste and high nutrition.[Methods]With natural wheat germ powder as the main raw material and maltodextrin,white sugar,compound stabilizer and other materials as auxiliary materials,the formula of wheat germ solid beverage was optimized using sensory evaluation value as an index,through the mixture experiment method and fuzzy mathematical analysis.[Results]The optimal formula of wheat germ solid beverage was:sugar 11.51%,maltodextrin 37.89%,wheat germ powder 50%,compound stabilizer 0.6%(arabic gum 0.3%,xanthan gum 0.3%),soya bean lecithin 0.2%,ethyl maltol 0.002%,and vanillin 0.003%.[Conclusions]This study provides a theoretical basis for expanding the market-oriented production and application of wheat germ.

Investigation of Essential or Non-essential Character of Some Hardly Known Trace Elements for Plants

The concentration distribution of essential and non-essential micro-elements of the tissues of healthy organisms shows significant difference. This fact can be used for clarification of the biological role of hardly known trace elements, as well, proving the essential or non-essential character. In case of essential elements the concentration range is rather narrow, the distribution is normal. In case of non-essential elements the interval is wide, the concentration-distribution is log-normal. Measurements and mathematical calculations were carried out for determination of the concentrations and concentration-distributions of some micro-elements, trying to clarify the essentiality or non-essential character of the investigated elements from point of view of plant physiology. Based on the measurements for radish Li and Ni seem to be non-essential trace elements, however in case of Sr the distribution curve suggests an essential character, because the concentration range is not wide.

Nonlinear Evolution Equations and Its Application to a Tumour Invasion Model

We consider nonlinear evolution equations with logistic term satisfying initial Neumann-boundary condition and show global existence in time of solutions to the problem in arbitrary space dimension by using the method of energy. Applying the result to a mathematical model of tumour invasion, we discuss the property of the rigorous solution to the model. Finally we will show the time depending relationship and interaction between tumour cells, the surrounding tissue and matrix degradation enzymes in the model by computer simulations. It is seen that our mathematical result of the existence and asymptotic behaviour of solutions verifies our simulations, which also confirm the mathematical result visibly.

Reasons in the Sino-West Philosophies and Critical and Creative Thinking Under the Cartesian Coordinate System

This paper provides a comparison and contrast of the rationality in the West and China.It is undergoing with the support of the Cartesian coordinate system.About 30 such figures illustrate the reason and causality of the philosophical concepts in question.The horizontal axis translates the independent variable,the cause;and the vertical elements interpret the effect.Such dynamic variable study supports the understanding of the core values in the Western and Chinese philosophy.On the other hand,there is a similar probing of the critical and creative thinking in the philosophy.Reflective thinking in varying fields with more perspective entails rational views.

A State Space Modeling of Non-Isolated Bidirectional DC-DC Converter with Active Switch

In this paper, analysis, design and implementation of non-isolated soft-switching bidirectional DC-DC converter with an active switch are described. The proposed topology gives the output voltage as twice as the input voltage and enhances the efficiency up to 94.5% and 92.9% for boost and buck mode operation by proper selection of the duty cycle. Soft switching can be achieved at both steps up and step down operating modes. Small signal analysis based on state space averaging and transfer functions have been presented in detail for the proposed converter. Finally, the feasibility of the desired converter is confirmed to mat lab simulation and investigational results.

PRINCIPLES AND PARAMETER DESIGN FOR AC-DC THREE-DEGREE FREEDOM HYBRID MAGNETIC BEARINGS

To simplify the mechanical structure, decrease the overall system size of the 3-degree freedom axial-radial magnetic bearings and reduce the manufacturing costs as well as operating costs, an innovated AC-DC 3-degree freedom hybrid magnetic bearing is proposed, which is driven by a DC amplifier in axial direction and a 3-phase power converter in radial directions respectively, and the axial and radial bias magnetic fluxes are provided with a common radial polarized permanent magnet ring. The principle producing magnetic suspension forces is introduced. By using equivalent magnetic circuit method, the calculation formulas of magnetic suspension forces and the mathematics models of the system are deduced. Nonlinearities of suspension forces and cross coupling between different degree freedoms are studied further by calculating the suspension forces at different displacements and control currents to validate the feasibility of the mathematics model. Then based on the mathematics models of the bearing, a control method of this novel bearing is designed. Lastly, the methods on parameter design and calculations of the bearing are presented, and an applicable prototype is simulated to analyze the magnetic path by using finite element analysis. The theory analysis and simulation results have shown that this magnetic bearing incorporates the merits of 3-phase AC drive, permanent magnet flux biased and axial-radial combined control, and reduces overall system size and has higher efficiency and lower cost, This innovated magnetic bearing has a wide application in super-speed and super-precision numerical control machine tools, bearingless motors, high-speed flywheels, satellites, etc.

Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components： the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms, while the third is described using a one-order differential equation and a radial-basis-function （RBF） network. For an aircraft configuration, the mathematical models of 6- component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynam- ics, respectively. The results show that： （1） unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; （2） unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and （3） unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected. It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability

QUALITATIVE ANALYSIS FOR A MATHEMATICAL MODEL OF AIDS

In this paper a mathematical model of AIDS is investigated.The conditions of the existence of equilibria and local stability of equilibria are given.The existences of transcritical bifurcation and Hopf bifurcation are also considered.in particular,the conditions for the existence of Hopf bifurcation can be given in terms of the coefficients of the characteristic equation.The method extends the application of the Hopf bifurcation theorem to higher differential equations which occur in biological models,chemical models,and epidemiological models etc.

Spatial Distribution of Hospitals in Handan City and Its Influencing Factors

Hospital is an important factor of people’s livelihood security,and the spatial layout of hospitals effectively ensures the medical convenience for residents.Location entropy and mathematical statistical analysis are used to study spatial distribution of hospitals.The results display that the distribution of medical facilities in Handan City is at a disadvantage level in Hebei Province,and medical facilities arr concentrated in the plain area.The layout of grade 3A hospitals in Hebei Province is characterized by urban centralization,and it is stronger in the east and weaker in the west.There is no medical facilities in Feixiang District of Handan City,and layout of medical facilities in Hanshan District and Congtai District is at advantage level of Handan City.The built-up area is the influencing factor for the distribution of medical resources.

The Distribution Search:An O(n) Expected Time Search

Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and experimental reesult proves that distribution search is superior to binary search.

Mass transport analysis of a showerhead MOCVD reactor

The mass transport process in a showerhead MOCVD reactor is mathematically analyzed.The mathematical analysis shows that the vertical component velocity of a point over the substrate is only dependent on vertical distance and is independent of radial distance.The boundary layer thickness in stagnation flow is independent of the radial position too.Due to the above features,the flow field suitable for film growth can be obtained.The ceiling height of the reactor has important effects on residence time and the mass transport process.The showerhead MOCVD reactor has a short residence time and diffusion plays an important role in axial transport,while both diffusion and convection are important in radial transport.

Object-Oriented Analysis of ELIMINO

ELIMINO is a mathematical research system developed for theimplementation of Wu's method, a powerful method for polynomial equation systemsolving and geometric theorem proving. The aim of ELIMINO is to provide usera programmable interpreting environment to use Wu's method in scientific researchand engineering computation. In this paper, the development of ELIMINo systemis outlined and the techniques adopted are discussed, then some details about theobject-oriented analysis of ELIMINO are presented.