数学学习方式的解析

中学生在常规学习中做数学课堂笔记存在很多问题,但要学好数学,必须养成良好的学习习惯,特别要注意认真记好、用好课堂笔记。文章就如何做好数学课堂笔记提出了一些思路和具体的操作策略。     

A psychometric analysis of residential location

Traditional housing needs studies focus on the trade-off between location and housing amenities. In most models, mode choice is viewed as conditional behavior in a given setting. New movers, however, select a new environment which includes a house, neighbourhood and transportation system. By using psychometric techniques, the attitudes and preferences of new movers to the suburbs of a large northeast city were analyzed to determine the relative importance in their selection process of the transportation characteristics of the new location. It was found that local and regional transportation and public transit played little role in selecting an apartment. There was no evidence of tradeoffs between travel time and living space postulated by urban economics. Most important to the choice process of these residents were internal characteristics of the apartment and pricing issues. This supports the idea that suburbanites chose to be captive auto users even when equivalent housing opportunities with transport alternatives are available. Implications for public transit and land use planning alternatives for the suburbs are discussed.     

基于重心法的应急物流中心选址初探

文章针对应急物流系统对时间的特殊要求,利用重心法建立了应急物流中心的选址模型。结果表明:重心法是一种简便、工作量较小的方法,能较好地简化应急物流中心的选址问题,具有较强的实用性。     

Integrating expected coverage and local reliability for emergency medical services location problems

Daskin's MEXCLP model [Daskin M. A maximum expected covering location model: formulation, properties, and heuristic solution. Transportation Science 1983;17:48-70] was one of the first efforts to capture the stochastic nature of emergency medical services (EMS) location problems within a mixed-integer formulation. With their subsequent introduction of MALP, ReVelle and Hogan [The maximum availability location problem. Transportation Science 1989;23:192-200] offered two key advances, local vehicle busyness estimates and the α-reliability objective. While these constructs have influenced many subsequent EMS location models, they have been subjected to relatively little empirical analysis. To address this, we introduce the LR-MEXCLP, a hybrid model combining the local busyness estimates of MALP with the maximum coverage objective of MEXCLP. We then solve a series of problems with all three models and employ simulation to estimate aggregate service levels. We find that LR-MEXCLP leads to modest but consistent service gains over both MALP and MEXCLP. These results support the merits of local busyness estimates, but they also suggest that the α-reliability objective may be inappropriate when seeking to maximize aggregate system response capabilities. More generally, our research underscores the utility of (a) linking modeling assumptions and goals with real-world application contexts, and (b) employing simulation or other techniques to validate theoretical results.     

Mathematical analysis applied to school attendance areas

The objective of this paper is to develop a generalized mathematical model of pupil assignment within school districts. This model can then be used to examine various policies of student integration. Proposed bussing schemes, school location policies, educational parks, attendance boundaries, etc., can be tested for cost, travel time or other measures of efficiency. Extension to other areas of educational planning is feasible.

Mathematical programming techniques are used to assign resources (say school children) to facilities (say schools) subject to restrictions on facilities (say capacity limits) and resources (say a maximum travel time or a desirable range of school “mixtures”) so that a measure of performance, the “objective function” (say total cost or total time of travel) is optimized. The model is intended to allow examination of a wide range of objective functions and system constraints.     

Efficiency analysis of emergency departments in metropolitan areas

The demand in the healthcare industry is increasing exponentially due to aging population of the world and this is leading to a rapid increase in the cost of healthcare. The emergency departments of the hospitals are the frontline of health care systems and play an additional critical role in providing an efficient and high-quality response for patients. The overcrowding at the emergency departments due to growing demand results in a situation where the demand for ED services exceeds the ability to provide care in a reasonable amount of time. This has led countries to reconsider their health policies in a way to increase their efficiency in their healthcare systems in general and in emergency departments, in particular. As in many countries, there has been a steady and significant increase in the number of patients that seek health services at the emergency departments of state hospitals of Turkey, due to the significant structural reforms in health services since 2003. While meeting this increasing demand, it is ever more important to provide these critical health services efficiently. Therefore, the efficiency of the emergency departments of seven general hospitals run by Istanbul's Beyoglu State Hospitals Association have been analyzed using categorical Data Envelopment Analysis (DEA) models. The analysis of DEA results is supported by a set of statistical methods to make it easier for the hospital administrators to interpret the analysis and draw conclusions. The analysis shows that less-equipped EDs are supported by better equipped, larger EDs, resulting in a hub-and-spoke type of structure among the EDs where “satellite” EDs serve an important referral function and thus evaluating their efficiency without taking the interoperability among these units into account would not be an accurate assessment of their performance.     

A robust optimization approach for decontamination planning of emergency planning zone: Facility location and assignment plan

Establishing a robust facility location and assignment plan to improve the efficiency of the decontamination process is critical to alleviating the physical impact of the radiation leakage that occurs in a nuclear accident. This study develops an approach for optimizing the locations of decontamination facilities and assignments of affected villages. The approach is a robust optimization model that optimizes the worst-case performance. The system dynamic model is integrated into the robust optimization model to simulate the decontamination process and compute the decontamination time. A case study is conducted of the Plume Emergency Planning Zone in China. The results indicate that (1) a decontamination site location plan can be obtained in which each site is located in a different direction, (2) no evacuee will be allowed to travel across the downwind area in an assignment plan, and (3) a larger financial investment does not imply an increased decontamination efficiency. An appropriate budget exists that can balance the decontamination time and cost. The proposed model can assist decision makers in (i) better understanding the effects of decontamination site location and village assignment and (ii) deciding which location and assignment plans should be applied to cope with disruptive nuclear accidents.     

Job location and the journey-to-work: An empirical analysis

In this paper we present and estimate a single equation model designed to explain the job-location behaviour of individuals living in a multi-centered metropolitan area. We test the model separately for heads of households and non-heads of households, as well as for the total working population, in order to isolate differences in commuting behaviour between primary and secondary wage earners. The relationships are estimated from 1971 Census, cross-section data using least squares multiple regression.The results of the location equation indicate that wage gradient variables are important determinants of job location for heads of households. On the other hand, non-heads are rather insensitive to the wage gradient. Rather, contrary to the decisions of heads, the job-location choices of non-heads are strongly influenced by socio-economic attributes, notably occupation, family size and age. Clearly, job-location decisions of primary wage earners (usually the household heads) are influenced by earnings-maximizing considerations while secondary earners (non-heads in general) put more weight on other socio-economic factors. The results also suggest that there is a hidden cost associated with uneven directional growth in the Toronto CMA. It is suggestive that urban planning strategies should reflect consideration of the greater desire or need for accessibility on the part of secondary wage earners (non-heads) and the need to balance residential and job opportunities at the extending margin of the urban area.     

A simulation-based methodology for optimization of ambulance service policies

A simulation-based methodology for the evaluation of the emergency ambulance system in the Vancouver, Canada, metropolitan area has been created. Outputs from the simulation of the system are utilized in the creation of the objective function of a branch and bound optimization procedure. The solutions are thus obtained at a significantly lower cost than if only simulation were used. The final solutions were verified by simulation runs.     

Expectations and industry location: a discrete time dynamical analysis

The new economic geography (NEG) aims to explain long-term patterns in the spatial allocation of industrial activities. It stresses that endogenous economic processes may enlarge small historic differences leading to quite different regional patterns—history matters for the long-term geographical distribution of economic activities. A pivotal element is that productive factors move to another region whenever the anticipated remuneration is higher in that region. Given the long-term nature of NEG analyses and the crucial role of expectations, it is astonishing that most of the existing models assume only naïve or myopic expectations. However, a recent stream of the literature in behavioral and experimental economics shows that agents often use expectational heuristics, such as trend extrapolating and trend reverting rules. We introduce such expectations formation hypotheses into a NEG model formulated in discrete time. This modification leads to a system of two nonlinear difference equations (corresponding, in the language of dynamical systems theory, to a 2-dimensional piecewise smooth map) and thus enriches the possible dynamic patterns: with trend extrapolating (reverting) the symmetric equilibrium is less (more) stable; and it may lose stability only via a flip bifurcation (or also via a Neimark–Sacker bifurcation) giving rise to a period-doubling cascade (or also to quasi-periodic orbits). In both cases, complex behavior is possible; multistability, that is, the coexistence of locally stable equilibria, is pervasive; and border-collision bifurcations are also allowed. In this sense, our analysis corroborates some of the basic insights of the NEG.     

Integrated fire and ambulance siting: A deterministic model

The model presented in this paper is developed for an integrated emergency system in which ambulance and fire service deployment are simultaneously considered. The model extends and blends the Maximal Covering Location Problem (MCLP) for ambulance siting and the Facility Location-Equipment Emplacement Technique (FLEET) for fire service placement. The objective of the new formulation is to maximize and trade-off both ambulance and fire coverage subject to constraints on the total number of vehicles and stations of both types that can be sited. We introduce a new concept in integrated coverage that permits free-standing ambulance stations to be sited in addition to fire stations. Typically, ambulances are located at fire stations and, sometimes, hospitals; that is, eligible sites are driven by prior choices that did not include consideration of ambulance service. Our results, based on three sample problems, suggest that, for a given budget level for facility construction, it may be possible for ambulance coverage to be increased with little or no loss in fire coverage. This condition pertains if ambulance stations are freed of the requirement to be sited only at fire stations.     

数学思维在数学建模课堂中的实践

学数学,用数学关键在于数学思维的培养,数学思维对于所有专业的大学生都是必不可少的。本文结合数学建模课堂教学,教师在教学中激发学生自己去学数学,提高数学建模实验能力,教学生学会学习,学会提出问题、分析问题、进而解决问题。学生学习应该既要学知识技能的数学更要学思想方法的数学。     

An application of a spatially distributed queuing model to an ambulance system

An application of a spatially distributed queuing model to an ambulance system is presented. The purpose of this research was to assess the usefulness of a variation of the “hypercube” queuing model developed specifically for modeling an ambulance system. The model was applied to the emergency medical system of Greenville County, South Carolina using historical data. Results indicate that the model provides reasonably accurate estimates of system performance measures when the input parameters can be accurately specified.     

Simulation modeling and optimization for ambulance allocation considering spatiotemporal stochastic demand

To ensure a timely response to emergencies, governments are obliged to implement effective ambulance allocation plans. In practice, an emergency medical service (EMS) system works in an uncertain environment, with stochastic demand, response-times, and travel-times. This uncertainty significantly affects ambulance allocation planning. However, few studies in this field adequately consider the effect of spatiotemporal uncertainty in demand, because it is difficult to measure it quantitatively. As a result, few analytic models capture the dynamic nature of an EMS system and, thus, the allocation plans they generate are not efficient in practice. Therefore, this study proposes a simulation-based optimization method for ambulance allocation. A simulation model is constructed to mimic the operational processes of an EMS system, and to evaluate the performance of an ambulance allocation plan in an uncertain environment. Gaussian mixture model clustering is used to derive the uncertain spatial demand. Then, the simulation generates emergency demand based on the obtained spatial distribution. A Gaussian-process-based search algorithm is used together with the simulation model to identify optimal solutions. To validate the proposed method, a case study is conducted using data on emergency patients in the Shanghai Songjiang District. Compared with the current plan adopted in Songjiang, the experimental results demonstrate that the delay time and frequency of the EMS system can be reduced significantly by employing the proposed methods. Furthermore, nearly 41% of the allocation cost can be saved.     

突发性公共事件的报道视角分析

随着媒体业的发达和日益现代化,发生在世界上的每一个重大突发性公共事件均成为各类媒体追逐的焦点.媒体担负着关注突发性事件、及时和客观地公开突发性事件信息的重要职责,在政府和群众之间起着沟通的"桥梁"作用.所以,媒体报道突发性公共事件需要特别注意正确的舆论导向,把握好报道的"度".只有这样,才能协助政府稳妥有效地处置突发性公共事件.