• The Mathematical Education
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• v.63 no.3
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• pp.393-409
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• 2024

The number line model, which intuitively marks numerical magnitudes in space, is widely utilized to help in understanding the magnitudes that fractions and decimals represent. The study analyzed 6^th graders' understanding of fractions and decimals, their problem solving strategies, and whether individual differences in the flexibility of various strategy uses are associated with the accuracy of numerical representation, calculation fluency, and overall mathematical achievement. As a result of the study, students showed relatively lower accuracy in representing fractions and decimals on a number line compared to natural numbers, especially for fractions with odd denominators compared to even denominators, and for two-digit decimals compared to three-digit decimals. Regarding strategy use, students primarily used benchmark, segmentation, and approximation strategies for fractions, and benchmark, rounding, and transformation strategies for decimals sequentially. Lastly, as students used various representation strategies for fractions, their accuracy in representing fractions and their overall mathematical achievement scores showed significantly better outcomes. Taken together, we suggest the need for careful instruction on different interpretations of fractions, the place value of decimals, and the meaning of zero in decimal places. Moreover, we discuss instructional methods that integrate the number line model and its diverse representation strategies to enhance students' understanding of fractions and decimals.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.95-126
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• 2009

The present contribution addresses the parallelization of advanced simulation methods for structural reliability analysis, which have recently been developed for large-scale structures with a high number of uncertain parameters. In particular, the Line Sampling method and the Subset Simulation method are considered. The proposed parallel algorithms exploit the parallelism associated with the possibility to simultaneously perform independent FE analyses. For the Line Sampling method a parallelization scheme is proposed both for the actual sampling process, and for the statistical gradient estimation method used to identify the so-called important direction of the Line Sampling scheme. Two parallelization strategies are investigated for the Subset Simulation method: the first one consists in the embarrassingly parallel advancement of distinct Markov chains; in this case the speedup is bounded by the number of chains advanced simultaneously. The second parallel Subset Simulation algorithm utilizes the concept of speculative computing. Speedup measurements in context with the FE model of a multistory building (24,000 DOFs) show the reduction of the wall-clock time to a very viable amount (<10 minutes for Line Sampling and ${\approx}$ 1 hour for Subset Simulation). The measurements, conducted on clusters of multi-core nodes, also indicate a strong sensitivity of the parallel performance to the load level of the nodes, in terms of the number of simultaneously used cores. This performance degradation is related to memory bottlenecks during the modal analysis required during each FE analysis.

• Journal of Distribution Science
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• v.15 no.6
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• pp.77-96
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• 2017

Purpose - This study aims to develop correspondence strategies to the environment change in domestic retail store types. Recently, new types of retails have emerged in retail industries. Therefore, trade area platform has developed focusing on the speed of data, no longer trade area from district border. Besides, 'trade area smart' brings about change in retail types with the development of giga internet. Thus, context shopping is changing the way of consumers' purchase pattern through data capture, technology capability, and algorithm development. For these reasons, the sales estimation model has been shown to be flawed using the notion of former scale and time, and it is necessary to construct a new model. Research design, data, and methodology - This study focuses on measuring retail change in large multi-shopping mall for the outlook for retail industry and competition for trade area with the theoretical background understanding of retail store types and overall domestic retail conditions. The competition among retail store types are strong, whereas the borders among them are fading. There is a greater need to analyze on a new model because sales expectation can be hard to get with business area competition. For comprehensive research, therefore, the research method based on the statistical analysis was excluded, and field survey and literature investigation method were used to identify problems and propose an alternative. In research material, research fidelity has improved with complementing research data related with retail specialists' as well as department stores. Results - This study analyzed trade area survival and its pattern through sales estimation and empirical studies on trade areas. The sales estimation, based on Huff model system, counts the number of households shopping absorption expectation from trade areas. Based on the results, this paper estimated sales scale, and then deducted modified probability model. Conclusions - In times of retail store chain destruction and off-line store reorganization, modified Huff model has problems in estimating sales. Transformation probability model, supplemented by the existing problems, was analyzed to be more effective in competitiveness business condition. This study offers a viable alternative to figure out related trade areas' sale estimation by reconstructing new-modified probability model. As a result, the future task is to enlarge the borders from IT infrastructure with data and evidence based business into DT infrastructure.