Value for Money and Prison Perimeters—Goal-programming for Gaols

A computer model has been developed to address the problem of attaining the most cost-effective balance when providing perimeter security at any given prison. The generalized analysis of security of perimeters (GASP) model evaluates the cost and performance of different prison perimeters in terms of several measures. The modelling process takes account not only of the site-specific problems such as perimeter shape, but also of the policy input of trade-offs between the various output measures of cost and effectiveness. Goal-programming and multi-criteria decision-making techniques have been used.     

An in-service primary teacher’s implementation of mathematical tasks: the case of length measurement and perimeter instruction

The purpose of this paper is to examine the cognitive demand levels of tasks used by an in-service primary teacher during length measurement and perimeter instruction and to examine a possible link between these tasks and the teacher’s mathematical knowledge in teaching. For this purpose, a case study approach was used and the data was drawn from classroom observations, semi-structured interviews, and field notes. Specific tasks from length measurement and perimeter instruction were presented and analyzed according to the Mathematical Tasks Framework. Then, how these tasks gave information about the teacher’s mathematical knowledge in teaching in the length measurement and perimeter topics was examined according to the Knowledge Quartet model. According to the findings of the study, the tasks used during length measurement and perimeter instruction were mostly categorized as low-level tasks. In addition, teacher’s mathematical knowledge in teaching affected the implementation of the tasks.     

Simulating student flow through a college of business for policy and structural change analysis

Under the pressure of sharp budget cuts and external demands for better performance, public institutions of higher education must examine how they can facilitate student graduation even as institutional resources diminish. This paper describes a computer model simulating the movement of undergraduates through a large, public college of business. The model allows changes in curriculum policy, prerequisite structure, and staffing capacity to be tested prior to implementation. Outcome measures focus primarily on the expected time to degree of two types of students who enter the university, first-time freshmen and upper division transfers, along with their respective 6-year and 4-year graduation rates. The validated model is used to experiment with both actual and potential scenarios facing the college and gauge their possible impact.     

Stochastic Simulation and Monte Carlo methods applied to the assessment of hydro-thermal generating system operation

Summary Simulation can be defined as a numerical technique for conducting experiments on a digital computer, which involves certain types of mathematical and logical models that describe the behaviour of a system over extended periods of real time. Simulation is, in a wide sense, a technique for performing sampling experiments on a model of the system. Stochastic simulation implies experimenting with the model over time including sampling stochastic variates from probability distributions. This paper describes the main concepts of the application of Stochastic Simulation and Monte Carlo methods to the analysis of the operation of electric energy systems, in particular to hydro-thermal generating systems. These techniques can take into account virtually all contingencies inherent in the operation of the system. Also, the operating policies that have an important effect on the performance of these systems can be realistically represented.     

Locality of the perimeter in Carnot groups and chain rule

In the class of Carnot groups, we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio–Kleiner–Le Donne, we show that the perimeter measure is local, i.e., that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. This solves a question left open in Ambrosio et al. (Calculus of variations: topics from mathematical heritage of Ennio De Giorgi. Quad Mat). As a consequence, we prove a general chain rule for BV functions in this setting.     

A two-dimensional numerical analysis of a small geometry MOSFET

This paper describes the development of a computer model to simulate small geometry metal-oxide-semiconductor field effect transistors (MOSFETs). The model is developed by obtaining computer generated solutions to the phenomenological equations which describe carrier transport and the electric fields in a semiconductor device. Threshold voltage variations and breakdown effects are also discussed.     

Resource Inputs and Performance Outputs in Social Security Offices

This paper describes a model of a Social Security office developed by the Operational Research Service of the DHSS. The model, based mainly on queueing theory, relates staffing levels, workloads, and productivity to performance measures based on customer delays. The paper describes the hypothesis underlying the model, the data requirements, technical details, and model calibration. Illustrative outputs of the model are presented and some uses of the model are briefly described.     

Real-time operational planning for the U.S. air traffic system

This paper describes an integrated planning model for the U.S. air traffic system. The approach incorporates the dual objectives of monitoring collision risk while minimizing transportation costs. Specialized solution algorithms exploit the underlying structure of the model—especially for large-scale examples. The proposed formulation is tested with real-world data for the Indianapolis control sector. Additional experiments with a CRAY X-MP/24 supercomputer show that a full-scale model can be solved under real time conditions. Despite these advances, additional work is required in developing a practical system. Suggestion are made for combining advances in computer graphics and mathematical modeling.     

Integrating modeling,algorithm design,and computational implementation to solve a large-scale non-linear mixed integer programming problem

This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business Decision Analysis, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712, USA.     

Flexible <Emphasis Type="Italic">versus</Emphasis> fixed timetabling: a case study

This case study presents the timetabling problem of the Flight Training Department at Embry-Riddle Aeronautical University. The problem consists of scheduling the flight resources to students to various time blocks. This problem represents a well-studied field in operations research, mainly adopting variations of mathematical programming models. This paper initially presents the efforts towards developing a fixed timetable using optimization models for the case under study. It is, however, demonstrated that implementation of optimum solutions obtained using this approach cannot be sustained, mainly because of the dynamic nature of the governing parameters. A flexible and dynamic timetable utilizing the university computer network, allowing the instructors and students to make their own decentralized flexible timetables, is proposed. A simulation study is initiated to compare the performance measures under both timetables. The analysis shows that implementation of a flexible system generates higher utilization of flight resources as well as improving key performance measures.     

SCAFFOLDING FOR SUCCESS: REFLECTIVE DISCOURSE AND THE EFFECTIVE TEACHING OF MATHEMATICAL THINKING SKILLS

This paper describes a research study into the teaching of mathematical thinking skills. Nine classes of students (in total) who had followed a course emphasising metacognitive skills outperformed their control groups on assessments of those skills and were also more successful on measures of their mathematical development. However, participant observation data revealed that there were important variations in teaching style between teachers and the success of their classes varied considerably. Observational data was used to classify the teaching styles into four groups. The teaching styles of the two most successful groups, the ‘dynamic scaffolders’ and the ‘reflective scaffolders’, are analysed here.     

Modelling a Solid-Waste Processing System by Discrete Event Simulation

This paper describes a discrete event simulation model for a solid-waste processing system which is to be installed in Zagreb, Croatia. The conceptual model was developed by activity cycle diagrams, and the computer model was developed using the program generation software package VS6. This paper describes the validation and verification of such a model, the design of simulation experiments and the selection of the system's configuration.     

Integrating modeling,algorithm design,and computational implementation to solve a large-scale nonlinear mixed integer programming problem

This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings. This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business Decision Analysis*, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712, USA.     

孔加工工序质量控制的研究

本文以孔加工工序为例,运用数理统计方法,吸收 Ｉ Ｓ Ｏ ９０００ 国际标准的管理思想,介绍了改进工序质量的措施     

Development of an Expert System: Translating Higher-Level Decisions into Lower-Level Aircraft Flights

This note describes two phases in the development of an expert system that translates European-wide directives into individual flight orders. This expert system was built for a military computer simulation, but parts of the logic can apply — and many of the illustrations in the text have been tailored — to creating and organizing commercial flights. The first phase of the development — a proof of principle expert system — emulated the logical deductions of an air traffic control supervisor or a flight planner. The second phase of development led to a working prototype decision support system that employed more mathematical comparisons of aircraft attributes than logical deductions.     

Didactic and theoretical-based perspectives in the experimental development of an intelligent tutorial system for the learning of geometry

This paper aims at showing the didactic and theoretical-based perspectives in the experimental development of the geogebraTUTOR system (GGBT) in interaction with the students. As a research and technological realization developed in a convergent way between mathematical education and computer science, GGBT is an intelligent tutorial system, which supports the student in the solving of complex problems at a high school level by assuring the management of discursive messages as well as the management of problem situations. By situating the learning model upstream and the diagnostic model downstream, GGBT proposes to act on the development of mathematical competencies by controlling the acquisition of knowledge in the interaction between the student and the milieu, which allows for the adaptation of the instructional design (learning opportunities) according to the instrumented actions of the student. The inferential and construction graphs, a structured bridge (interface) between the contextualized world of didactical contracts and the formal computer science models, structure GGBT. This way allows for the tutorial action to adjust itself to the competential habits conveyed by a certain classroom of students and to be enriched by the research results in mathematical education.     

Students encountering obstacles using a CAS

The paper describes a pilot study on the use of computer algebra at upper secondary level. A symbolic calculator was introduced in a pre-examination class studying for advanced pre-university mathematics. With the theoretical framework of Realistic Mathematics Education and Developmental Research as a background, the study focused on the identification of obstacles that students encountered while using computer algebra. Five obstacles were identified that have both a technical and a mathematical character. It is the author's belief that taking these barriers seriously is important in developing useful pedagogical strategies.This revised version was published online in September 2005 with corrections to the Cover Date.     

Use of computer modelling in the long-range planning for extended library services

This paper describes the development and implementation of a computer simulation model designed as an aid to the human decision-maker responsible for developing plans to extend library services to geographical areas now unserved. An application to a planning region in the state of Washington is presented.     

Report on Survey of Mathematical Sciences and Social Sciences∗

The computer offers the possibility of allowing students to explore mathematical ideas, but for them to become fluent in the use of existing model‐building languages makes excessive demands on many students. The paper describes an attempt to overcome this fluency barrier by allowing students to express their ideas for models in a friendly environment. Whilst the language MODL relieves the students of complex numerical methods, it does not take away the need for them to formulate a model in a logical and consistent way. To aid software portability the language is written in BASIC and was developed on a microcomputer with good graphical display characteristics.