(Please read "Format Specification for Papers of the National Mathematical Modeling Competition for College Students" first)
Analysis of Heavy Metal Pollution in Urban Topsoil
With the rapid development of urban economy and the continuous increase of urban population, the impact of human activities on urban environmental quality has become increasingly prominent. The verification of urban soil geological environment anomalies, and how to use the massive data obtained from the verification to carry out urban environmental quality evaluation and study the evolution mode of urban geological environment under the influence of human activities have increasingly become the focus of attention.
According to the functional division, urban areas can generally be divided into living areas, industrial areas, mountainous areas, main roads and parks, and divided into 1 area, 2 areas, ... and 5 areas. Different regional environments are affected by human activities to different degrees.
The soil geological environment of a city was investigated. Therefore, the investigated urban area is divided into grid areas with the spacing of about 1 km, and the surface soil (0 ~ 1 0 cm depth) is sampled and numbered according to each square kilometer1sampling point, and the positions of sampling points are recorded by GPS. The concentration data of various chemical elements contained in each sample are obtained by testing and analyzing with special instruments. On the other hand, samples are taken from natural areas 2 kilometers away from people and industrial activities as background values of elements in urban topsoil.
Attachment 1 lists the location, altitude and functional area of the sampling point, attachment 2 lists the concentrations of eight major heavy metal elements at the sampling point, and attachment 3 lists the background values of eight major heavy metal elements.
Now you are required to complete the following tasks through mathematical modeling:
(1) The spatial distribution of eight main heavy metal elements in urban areas is given, and the pollution degree of heavy metals in different areas of urban areas is analyzed.
(2) Through data analysis, the main reasons of heavy metal pollution were explained.
(3) Analyze the propagation characteristics of heavy metal pollutants and establish a model to determine the location of pollution sources.
(4) Analyze the advantages and disadvantages of your model, and what information should be collected in order to better study the evolution model of urban geological environment? With this information, how to build a model to solve the problem?
20 1 1 Higher Education Club Cup National Mathematical Modeling Competition for College Students
(Please read "Format Specification for Papers of the National Mathematical Modeling Competition for College Students" first)
Question B: Setting and Scheduling of Traffic Patrol Service Platform
"Call the police when you are in trouble" is a well-known buzzword. The police shoulder four functions: criminal law enforcement, public security management, traffic management and serving the masses. In order to realize these functions more effectively, it is necessary to set up traffic patrol service platforms in some traffic arteries and important parts of the city. The functions and police force of each traffic patrol service platform are basically the same. Due to the limited police resources, how to reasonably set up the traffic patrol service platform, allocate the jurisdiction of each platform and dispatch police resources according to the actual situation and needs of the city is a realistic topic faced by the public security department.
Try to establish a traffic patrol service platform in a city, and establish a mathematical model to analyze and study the following problems:
(1) The attached figure 1 in annex 1 gives a schematic diagram of the traffic network in downtown A and the existing 20 traffic patrol service platforms. See Annex 2 for relevant data and information. Please assign jurisdiction to each traffic patrol service platform, so that a traffic patrol (with a police car speed of 60km/h) can arrive at the incident site within 3 minutes as far as possible when an emergency occurs within the jurisdiction.
For major emergencies, it is necessary to dispatch the police resources of 20 traffic patrol service platforms in the whole region to achieve a rapid and comprehensive blockade of the access area 13 traffic arteries. In fact, the police force on a platform blocks at most one intersection. Please give a reasonable scheduling scheme for the police force of the traffic patrol service platform in this area.
In view of the unbalanced workload of the existing traffic patrol service platform and the long police time in some places, it is planned to add 2 to 5 more platforms in this regard. Please confirm the specific number and location of platforms to be added.
(2) According to the specific situation of the whole city (six districts of A, B, C, D, E and F in the main city), according to the principles and tasks of setting up the traffic patrol service platform, analyze and study the rationality of the existing traffic patrol service platform in this city (see Annex). If it is obviously unreasonable, please give a solution.
If a major criminal case occurs in the city's location P (node P(32), an alarm is received 3 minutes after the incident, and the suspect has fled by car. In order to quickly search for suspects, please give the best containment scheme for dispatching police resources on the municipal traffic patrol service platform.
Attachment1:Schematic diagram of traffic network and platform setting in Area A and City Six.
Attachment 2: Data sheets related to traffic network and platform setting in the sixth district of the city (***5 worksheets).