• Communications of Mathematical Education
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• v.29 no.3
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• pp.533-551
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• 2015

Problem posing in school mathematics is generally regarded to make a new problem from contexts, information, and experiences relevant to realistic or mathematical situations. Also, it is to reconstruct a similar or more complicated new problem based on an original problem. The former is called as problem generation and the latter is as problem reformulation. The purpose of this study was to explore the co-relation between problem generation and problem reformulation, and the educational effectiveness of each problem posing. For this purpose, on the subject of 33 pre-service secondary school teachers, this study developed two types of problem posing activities. The one was executed as the procedures of [problem generation${\rightarrow}$solving a self-generated problem${\rightarrow}$reformulation of the problem], and the other was done as the procedures of [problem generation${\rightarrow}$solving the most often generated problem${\rightarrow}$reformulation of the problem]. The intent of the former activity was to lead students' maintaining the ability to deal with the problem generation and reformulation for themselves. Furthermore, through the latter one, they were led to have peers' thinking patterns and typical tendency on problem generation and reformulation according to the instructor(the researcher)'s guidance. After these activities, the subject(33 pre-service teachers) was responded in the survey. The information on the survey is consisted of mathematical difficulties and interests, cognitive and affective domains, merits and demerits, and application to the instruction and assessment situations in math class. According to the results of this study, problem generation would be geared to understand mathematical concepts and also problem reformulation would enhance problem solving ability. And it is shown that accomplishing the second activity of problem posing be more efficient than doing the first activity in math class.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.1
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• pp.13-27
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• 2014

In this paper, we deal with a Steiner Ring Star (SRS) problem arising from the design of survivable telecommunication networks. We develop two mixed integer programming formulations for the SRS problem by implementing Miller-Tucker-Zemlin (MTZ) and Sarin-Sherali-Bhootra (SSB) subtour elimination constraints, and then apply the reformulation-linearization technique (RLT) to enhance the lower bound obtained by the LP relaxation. By exploiting the ring-star structure of underlying network, we devise some valid inequalities that tighten the LP relaxation. Computational results demonstrate the effectiveness of the proposed solution procedure.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.232-232
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• 1992

• The Mathematical Education
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• v.57 no.3
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• pp.289-309
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• 2018

There has been a gradually increasing focus on adopting mathematical modeling techniques into school curricula and classrooms as a method to promote students' mathematical problem solving abilities. However, this approach is not commonly realized in today's classrooms due to the difficulty in developing appropriate mathematical modeling problems. This research focuses on developing reformulation strategies for those problems with regard to mathematical modeling. As the result of analyzing existing textbooks across three grade levels, the majority of problems related to the real-world focused on the Operating and Interpreting stage of the mathematical modeling process, while no real-world problem dealt with the Identifying variables stage. These results imply that the textbook problems cannot provide students with any chance to decide which variables are relevant and most important to know in the problem situation. Following from these results, reformulation strategies and reformulated problem examples were developed that would include the Identifying variables stage. These reformulated problem examples were then applied to a 7th grade classroom as a case study. From this case study, it is shown that: (1) the reformulated problems that included authentic events and questions would encourage students to better engage in understanding the situation and solving the problem, (2) the reformulated problems that included the Identifying variables stage would better foster the students' understanding of the situation and their ability to solve the problem, and (3) the reformulated problems that included the mathematical modeling process could be applied to lessons where new mathematical concepts are introduced, and the cooperative learning environment is required. This research can contribute to school classroom's incorporation of the mathematical modeling process with specific reformulating strategies and examples.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.141-149
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• 1998

One of the difficulties in using the current Boolean-based information retrieval systems is that it is hard for a user, especially a novice, to formulate an effective Boolean query. One solution to this problem is to let the system formulate a query for a user from his relevance feedback documents in this research, an intelligent query reformulation mechanism based on ID3 is proposed and the sensitivity of its retrieval effectiveness, i.e., recall, precision, and E-measure, to various input settings is analyzed. The parameters in the input settings is the number of relevant documents. Experiments conducted on the test set of Medlars revealed that the effectiveness of the proposed system is in fact sensitive to the number of the initial relevant documents. The case with two or more initial relevant documents outperformed the case with one initial relevant document with statistical significances. It is our conclusion that formulation of an effective query in the proposed system requires at least two relevant documents in its initial input set.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.525-529
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• 1996

Decision environments involve a high degree of uncertainty as well as multiple, conflicting goals. Although traditional goal programming offers a means of considering multiple, conflicting goals and arrives at a satisficing solution in a deterministic manner, its major drawback is that decision makers often specify aspiration level of each goal as a single number. To overcome the problem of setting aspiration levels, chance constrained programming can be incorporated into goal programming formulation so that sampling information can be utilized to describe uncertainty distribution. Another drawback of goal programming is that it does not provide a systematic approach to set priorities and trade-offs among conflicting goals. To overcome this weekness, the analytic hierarchy process(AHP) is used in the model. Also, most goal programming models in the literature are of a linear form, although some nonlinear models have been presented. Consideration of risk in technological coefficients and right hand sides, however, leads to nonlinear goal programming models, which require a linear approximation to be solved. In this paper, chance constrained reformulation with linear approximation is presented for a 0-1 goal programming problem whose technological coefficients and right hand sides are stochastic. The model is presented with a numerical example for the purpose of demonstration.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.486-490
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• 1993

This paper presents an improved algorithm which enables to find a suboptimal $H^{\infty}$ controller. In the $H^{\infty}$ control problem with output multiplicative uncertainty, the Glover-Doyle algorithm has sorne constraints for the standard plant. The proposed algorithm removes them by reformulating the standard plant. We show the validity of this algorithm by investigating the variation of norm-bound.d.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.141-152
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• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.

• The Transactions of the Korea Information Processing Society
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• v.2 no.3
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• pp.417-424
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• 1995

This paper describes MFT(Mean Field Theory) neural network with continuous with continuous variables is applied to quantification analysis problem. A quantification analysis problem, one of the important problems in statistics, is NP complete and arises in the optimal location of objects in the design space according to the given similarities only. This paper presents a MFT neural network with continuous variables for the quantification problem. Starting with reformulation of the quantification problem to the penalty problem, this paper propose a "one-variable stochastic simulated annealing(one-variable SSA)" based on the mean field approximation. This makes it possible to evaluate of the spin average faster than real value calculating in the MFT neural network with continuous variables. Consequently, some experimental results show the feasibility of this approach to overcome the difficulties to evaluate the spin average value expressed by the integral in such models.ch models.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4678-4702
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• 2018

Traffic Matrix estimation has always caught attention from researchers for better network management and future planning. With the advent of high traffic loads due to Cloud Computing platforms and Software Defined Networking based tunable routing and traffic management algorithms on the Internet, it is more necessary as ever to be able to predict current and future traffic volumes on the network. For large networks such origin-destination traffic prediction problem takes the form of a large under- constrained and under-determined system of equations with a dynamic measurement matrix. Previously, the researchers had relied on the assumption that the measurement (routing) matrix is stationary due to which the schemes are not suitable for modern software defined networks. In this work, we present our Compressed Sensing with Dynamic Model Estimation (CS-DME) architecture suitable for modern software defined networks. Our main contributions are: (1) we formulate an approach in which measurement matrix in the compressed sensing scheme can be accurately and dynamically estimated through a reformulation of the problem based on traffic demands. (2) We show that the problem formulation using a dynamic measurement matrix based on instantaneous traffic demands may be used instead of a stationary binary routing matrix which is more suitable to modern Software Defined Networks that are constantly evolving in terms of routing by inspection of its Eigen Spectrum using two real world datasets. (3) We also show that linking this compressed measurement matrix dynamically with the measured parameters can lead to acceptable estimation of Origin Destination (OD) Traffic flows with marginally poor results with other state-of-art schemes relying on fixed measurement matrices. (4) Furthermore, using this compressed reformulated problem, a new strategy for selection of vantage points for most efficient traffic matrix estimation is also presented through a secondary compression technique based on subset of link measurements. Experimental evaluation of proposed technique using real world datasets Abilene and GEANT shows that the technique is practical to be used in modern software defined networks. Further, the performance of the scheme is compared with recent state of the art techniques proposed in research literature.