我国第三产业与消费和交通电讯业关系的统计分析及其发展战略探讨

本文以生产函数理论为基础 ,根据第三产业、消费和交通电讯业的统计数据建立第三产业数学模型 ,定量地分析第三产业发展决策 ,阐明我国第三产业发展规模、速度及方向     

Understanding secondary–tertiary transition in mathematics

In Clark and Lovric (Suggestion for a theoretical model for secondary–tertiary transition in mathematics, Math. Educ. Res. J. 20(2) (2008), pp. 25–37) we began developing a model for the secondary–tertiary transition in mathematics, based on the anthropological notion of a rite of passage. We articulated several reasons why we believe that the educational transition from school to university mathematics should be viewed (and is) a rite of passage, and then examined certain aspects of the process of transition. Present article is a continuation of our study, resulting in an enhanced version of the model. In order to properly address all aspects of transition (such as a number of cognitive and pedagogical issues) we enrich our model with the notions of cognitive conflict (conceptual change) and culture shock (although defined and used in contexts that differ from the transition context, nevertheless, we found these notions highly relevant). After providing further justification for the application of our model to transition in mathematics, we discuss its many implications in detail. By critically examining current practices, we enhance our understanding of the many issues involved in the transition. The core section ‘Messages and implications of the model’ is divided into subsections that were determined by the model (role of community, discontinuity of the transition process, shock of the new, role of time in transition, universality of transition, expectations and responsibilities, transition as a real event). Before making final conclusions, we examine certain aspects of remedial efforts.     

A perturbation solution for bacterial growth and bioremediation in a porous medium with bio-clogging

We investigate a flow problem of relevance in bioremediation and develop a mathematical model for transport of contamination by groundwater and the spreading, confinement, and remediation of chemical waste. The model is based on the fluid mass and momentum balance equations and simultaneous transport and consumption of the pollutant (hydrocarbon) and nutrient (oxygen). Particular emphasis is placed on the study of processes involving the full coupling of reaction, transport and mechanical effects. Dimensional analysis and asymptotic reduction are used to simplify the governing equations, which are then solved numerically.     

湖南省第三产业就业人数预测——基于灰色系统GM(1,1)模型

运用灰色系统GM(1,1)模型对2002-2007年湖南省第三产业就业人数的数据进行分析.通过灰色系统相关检验发现,GM(1,1)模型误差较小,能较好地拟合湖南省第三产业就业人数的情况.运用该模型预测:2008年湖南省第三产业就业人数是1403.4万人,2009年是1512.2万人,2010年是1629.3万人,2011年是1755.6万人.     

Applying GIS and Combinatorial Optimization to Fiber Deployment Plans

A decision-support system for the Fiber Deployment Plan problem is developed for the telephone cable network design in the telecommunications industry. The system employs a Geographic Information System (GIS) and uses combinatorial optimization techniques as its components. A mathematical combinatorial optimization model is formulated for the problem and a heuristic solution procedure is developed for the model. A GIS within the ESRI Arc/INFO and ArcView environment is used to provide data needed to build the mathematical combinatorial optimization model and to furnish an interface between the users and computers in data input and in solution result display. Combinatorial optimization techniques are used in the heuristic solution procedure to find good solutions for the optimization model. The developed decision-support system has been used to real life problems and has resulted in tremendous improvements in the telephone cable network design process. The user is completely satisfied with the performance of the system.     

基于超效DEA模型的泛珠三角区第三产业生产效率评价

基于超效DEA模型的方法,选取了从1998年至2010年的第三产业投入产出数据,分析了泛珠三角区9个省第三产业效率并进行评价.通过对9个省的第三产业生产效率的横向对比发现四川省第三产业生产效率最高,并对四川省第三产业生产效率进行分解研究,总结了四川省所采取的有利于第三产业技术进步和规模效率提高的政策措施.对泛珠三角区内其它各省第三产业发展提出了相应建议.     

Computer-aided design of synchronous generators with comb rotors

A mathematical model of a synchronous generator with comb rotor is implemented in a computer-aided design (CAD) package. The model integrates the differential equations characteristic of an electric machine; tabled data and empirical coefficients; and geometric, electromagnetic, and economic parameters of machine design. The complexity of the model requires that the solution procedure adopt a naive random search methodology, and an expert system is integrated within the package. The expert system is used mainly for guidance, and the priority of initial parameter values is delegated to the designer. An illustrative example is described to demonstrate the methodology of the computer-aided design procedure.     

Some inverse problems of internal-diffusion kinetics of adsorption

Methods are proposed for determining the diffusion coefficients of adsorbed molecules and the adsorption isotherms from given concentrations of the solutes in the external solution. The methods are based on a comparison of experimental data with the numerical results produced by a mathematical model of internal-diffusion kinetics of adsorption from a constant bounded volume.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 41–46, 1988.     

Optimal Design of Hole Reinforcements for Composite Structures

In many technical applications like aerospace and automotive structures, holes in thin-walled composite components are necessary for some reason. It easily happens that the presence of a hole results in a detrimental stress concentration in the vicinity of the hole with a strength degradation and premature failure of the structure, respectively. In order to avoid the aforementioned overloading and to achieve a sufficient strength, in practice, a local reinforcement is employed. In the present study, reinforcements by elliptic doublers,as well as doublers adapted to reinforcement requirements in a layerwise manner, are considered. The increasing demands of a low weight and high strength for modern structures lead to the problem of an optimal reinforcement design. For this purpose, an appropriate optimization model is set up, a structural model is developed to describe the mechanical behavior (displacements, stresses, etc.) of such structures, and the techniques of mathematical structural optimization are used to find an optimal design in a systematic manner. In this study, the finite-element method is applied to the structural analysis. Eventually, an appropriate mathematical optimization algorithm is used to approach the desired design optimum in an iterative way. The implemented procedure works with a good reliability and efficiency and yields optimal reinforcement designs which are very useful for direct engineering applications.     

The design of a full-scale industrial mineral leaching process

The movement of water through the ground is of great industrial importance, and has applications in mining. This paper uses a mathematical model for groundwater flow to present a new design methodology for in situ leaching of minerals. This is a process in which a lixiviant (a solution capable of dissolving the mineral of interest) is pumped into a mineral-bearing rock in order to dissolve the mineral at its own location within the rock itself. The fluid is then pumped to the surface and the mineral is recovered chemically. A major problem with this technology comes from the need to predict accurately where the leaching fluid will go within the ore. Of particular concern is the need to recover as much of the fluid as possible at an appropriate later time. This paper proposes a design strategy that enables the complete recovery of all the mineral leaching fluid, in a full-scale three-dimensional operation. It relies on a spatially periodic arrangement of injection and recovery wells, with a type of secondary recovery process using injected water. The mathematical problem for homogeneous rock is posed, and an extremely accurate asymptotic solution is given. This is sufficient for experimental design purposes. In addition, the full problem is solved numerically using a boundary-integral approach, to investigate limiting cases.     

Mathematical model and optimum design approach of sinusoidal pressure wave generator for downhole drilling tool

Mud pulse generators have been widely used for the real-time transmission of valuable directional and formation data from downholes with depths of thousands of meters. There have been numerous studies on the design of mud pulse generators in which the pressure waves were typically nonsinusoidal. Sinusoidal waves provide improved long-distance data transmission and signal noise suppression compared with nonsinusoidal waves. Although sinusoidal pressure wave generators have been studied in the published literature, the influence of the risks of clogging on the design of the generator for producing sinusoidal pressure waves has rarely been considered. To generate sinusoidal pressure waves and to reduce the risks of clogging, a mathematical model for the design of a sinusoidal pressure wave generator is developed in this paper. The effects of the axial and radial clearances between the rotor and stator on the design of the generator are considered in the model. An optimum design method for the generator is provided by combining the developed model and a computational fluid dynamics analysis. Finally, an experimental platform was built and experiments at frequencies 2 Hz and 10 Hz were conducted to validate the design result. The simulation and experimental results show that the optimized pressure waves closely approximate sine waves. Therefore, the developed mathematical model and optimization approach can be used to design a sinusoidal pressure wave generator.     

Determination of surface singularities of a cycloidal gear drive with inner meshing

The cycloidal gear drive is widely used in industrial applications, such as gerotor pump, speed reducer, transmission apparatus and so on. In this paper, the profile of inner rotor is with equidistance to an epitrochoidal (or extended epicycloid) curve, and the mathematical model of the internal cycloidal gear with tooth difference is created by the theory of gearing. The proposed mathematical model can simulate not only gerotor pump but also cycloidal speed reducer. The design of outer rotor depends on different applications. Being applied to the speed reducer, the outer rotor will be a pin wheel (outer rotor arc teeth). Besides, for a better design of the gerotor pump, the mathematical model of the generated shape between outer rotor arc teeth will also be proposed. Lastly, a simpler dimensionless equation of undercutting will be derived from the proposed mathematical model. And a more explicit procedure to determine the feasible design region without undercutting on the tooth profile or interference between the pins will be developed and demonstrated by some numerical examples.     

Optimizing biological wastewater treatment

Ricerche di Matematica - In this paper we propose a non linear mathematical model describing the process of biodegradation of organic pollutants by means of fungi, and using glucose to sustain its...     

Mathematical modelling of the oxygen uptake kinetics during whole-body endurance exercise and recovery

In this study, we elucidate four different mathematical models of the kinetics of oxygen uptake during whole-body endurance exercise at different intensities and throughout the subsequent recovery periods. We employ the hypothetical inductive–deductive method and forecast four different models for the oxygen kinetic. The VO₂ development using these models compared with experimental results where an elite cross-country skier performed laboratory tests while running with poles on a treadmill, in which the rate of oxygen uptake and blood lactate concentration as a function of time were measured. The most developed model accounted for the delayed superimposed slow component of oxygen uptake and the influence of lactic power production on the oxygen kinetics. The rate of change in oxygen with this model is consistent with the accumulated oxygen deficit model and matched the data well, even for intensities above the lactate threshold and during recovery.     

A model of the effects of nonuniform soil-water distribution on the subsurface migration of bacteria: Implications for land disposal of sewage

Australia produces one of the highest volumes of agricultural, industrial, and municipal wastes per capita in the world. Increasingly, the public is demanding statutory authorities investigate environmentally sound methods of land application. However, a real danger associated with land disposal of wastes, in particular sewage, is the possible contamination of groundwater and threats to public health resulting from transport of pathogenic micro-organisms through the vadose zone. The study of the transport and fate of micro-organisms in soils is also of vital importance in the fields of oil recovery, biological control of plant root diseases, and in-situ bioremediation of contaminated soils and aquifers from industrial accidents. The objectives of this paper are

• 1.(a) to explore the extent of spatial and temporal heterogeneity found in the soil-water patterns in Australian soils, and
• 2.(b) to establish the framework for a mathematical model of the population dynamics and mobility of soil bacterial transport through the unsaturated zone of soils.

The model explicitly incorporates spatial and temporal heterogeneity in describing these dynamics.     

Experimental versus numerical data for breast cancer progression

This paper deals with a mouse model of breast cancer based on two mammary adenocarcinoma cell lines derived from a spontaneous tumor of the mammary gland in a female BALB/c mouse. We investigate both animal and mathematical models of tumor progression, and demonstrate a correspondence between the experimental and predicted data. The mathematical model is solved numerically and the laboratory data are utilized in order to find unknown parameters for the model equations. The results of the numerical experiments illustrate that the mathematical model has a potential to describe the growth of cancer cells in vivo.     

Computational approaches to parameter estimation and model selection in immunology

One of the significant challenges in biomathematics (and other areas of science) is to formulate meaningful mathematical models. Our problem is to decide on a parametrized model which is, in some sense, most likely to represent the information in a set of observed data. In this paper, we illustrate the computational implementation of an information-theoretic approach (associated with a maximum likelihood treatment) to modelling in immunology.The approach is illustrated by modelling LCMV infection using a family of models based on systems of ordinary differential and delay differential equations. The models (which use parameters that have a scientific interpretation) are chosen to fit data arising from experimental studies of virus-cytotoxic T lymphocyte kinetics; the parametrized models that result are arranged in a hierarchy by the computation of Akaike indices. The practical illustration is used to convey more general insight. Because the mathematical equations that comprise the models are solved numerically, the accuracy in the computation has a bearing on the outcome, and we address this and other practical details in our discussion.     

Numerical solution of an inverse problem for a two-dimensional mathematical model of sorption dynamics

We consider a two-dimensional mathematical model of sorption that allows for inner-diffusion kinetics as well as longitudinal and transverse diffusion. The inverse problem of determining the sorption isotherm from an experimental dynamic output curve is investigated for this model and stable solution methods are proposed for the inverse and the direct problem. The efficiency of the solution methods is explored in computer experiments.     

A multi-modal approach to the location of a rapid transit line

The location of a rapid transit line (RTL) represents a very complex decision problem because of the large number of decision makers, unquantifiable criteria and uncertain data. In this context Operational Research can help in the design process by providing tools to generate and assess alternative solutions. For this purpose two bicriterion mathematical programming models — the Maximum Coverage Shortest Path model and the Median Shortest Path model — have been developed in the past. In this paper a new bicriterion model, which can evaluate in a more realistic way the attractivity of an RTL is introduced. To calculate an estimation of the non-inferior solution set of the problem, a procedure based on a k-shortest path algorithm was developed. This approach was applied to a well-known sample problem and the results are discussed and compared with those obtained using a Median Shortest Path model.     

A simple elemental continuity based model application to study the anaerobic microbial activity for the treatment of dairy manure

A simple anaerobic digestion (AD) model was formulated with emphasis on understanding the microbial activity during AD. The model was formulated according to two main rules that regulate the microbial growth. The first rule was maintaining the elemental continuity of macronutrients C, H, N, O, P, and S. The second rule satisfied the thermodynamics of the main AD catabolic reactions: acidogenesis and both acetotrophic and hydrogenotrophic methanogenesis. Accordingly, the stoichiometric parameters were evaluated as functions of the bacterial yield. The model also considered the enzymatic hydrolysis of solid waste. For a known solid waste composition, experimental data was utilized to estimate microbial initial concentrations, yields and kinetics, i.e., to achieve better understanding of the main AD microbial activity. The model was applied to three sets of batch experiments focusing on anaerobic dairy manure degradation. The model predicted the degradation dynamics, estimated the bacterial concentration in different inoculums, and evaluated the effect of inoculum ratios in speeding up the degradation. Elemental continuity based formulation of the model evaluated additional components that are necessary for future studies of macronutrients recovery, limitation/toxic effects, and chemical equilibrium.