• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.291-300
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• 1999

The Snyder's synthetic unit hydrograph method is selected to apply the concept of the fractal dimension by stream order for the practicable rainfall-runoff generation, and fourth types of the Snyder's relation are derived from topographic and observed unit hydrograph data of twenty-nine basins. As a result of the analysis of twenty-nine basins and the verification of two basins, the Snyder's relation which considers the fractal dimension of the stream length and uses calculated unit hydrograph data shows the best result. The concept of the fractal dimension by stream order is applied to the Snyder's synthetic unit hydrograph method. The topographic factors, used in the Snyder's synthetic unit hydrograph method, which have a property of the stream length like $L_{ma}$ (mainstream length) and $L_{ca}$ (length along the mainstream to a point nearest the watershed centroid) were considered. In order to simplify the fractal property of stream length, it is supposed that $L_{ma}$ has not the fractal dimension and the stream length between $L_{ma}$ and ($L_{ma}\;-\;L_{ca}$) has the fractal dimension of 1.027. From the utilization of this supposition, a new Snyder's relation which consider the fractal dimension of the stream length occurred by the map scale used was finally suggested.

• Journal of Educational Research in Mathematics
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• v.13 no.1
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• pp.57-75
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• 2003

The goal of this paper is to offer material which make mathematising Fruedenthal(1991) proposed be experienced through the process of teaching and learning mathematics. In this paper, the number of unit squares a diagonal passes through for an m$\times$n lattice rectangle is studied and its generalization is discussed. Through this discussion, the adaptability of this material Is analysed. Especially, beyond inductional conjecture, the number of unit squares is studied by more complete way, and generalization in 3-dimension and 4-dimension are tried. In school mathematics, it is enough to generalize in 3-dimension. This material is basically appropriate for teaching and learning mathematising in math classroom. In studying the number of unit squares and unit cubes, some kinds of mathematising are accompanied. Enough time are allowed for students to study unit squares and unit cubes to make them experience mathematising really. To do so, it is desirable to give students that problem as a task, and make them challenge that problem for enough long time by their own ways. This material can be connected to advanced mathematics naturally in that it is possible to generalize this problem in n-dimension. So, it is appropriate for making in-service mathematics teachers realize them as a real material connecting school mathematics and advanced mathematics.

• Water Engineering Research
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• v.1 no.4
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• pp.279-291
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• 2000

A mathematical model using dynamic programming approach is applied to an optimal unit commitment problem. In this study, the units are treated as stages instead of as state dimension, and the time dimension corresponds to the state dimension instead of stages. A considerable amount of computer time is saved as compared to the normal approach if there are many units in the basin. A case study on the Lower Colorado River Basin System is presented to demonstrate the capabilities of the optimal scheduling of hydropower units.

• Journal of architectural history
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• v.31 no.3
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• pp.7-16
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• 2022

Fen(分°) is the proportional dimension unit of the standard timber section on Yingzaofashi(營造法式), and there is a phrase that not only structural members but the whole structural design of a building also use Fen as the dimension unit on the book. But in fact only the section dimensions of structural members are recorded by Fen, but the design dimensions are recorded by Chi(尺) on the book. Other historical records also described the building size by Chi. So there has been long-standing debate on the phase in Chinese architectural history society, including the recent confrontation on the analysis of survey figures of the east great hall of Foguangsi temple(佛光寺 東大殿). This paper analyzes all the records about the size of structural members and section planning on the book to make various calculation and evaluation. And it makes a survey of Cai(材) as the dimension and design unit between Chi and Fen through geometric analysis. Cai might be a rough unit of measurement in terms of structural and proportional scheming on Yingzaofashi, and the full size Cai(足材) had been a building scheming module before the Song dynasty.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.245-250
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• 2009

We consider a code function from the unit interval which has a generalized dyadic expansion into a coding space which has an associated ultra metric. The code function is not a bi-Lipschitz map but a dimension-preserving map in the sense that the Hausdorff and packing dimensions of any subset in the unit interval and its image under the code function coincide respectively.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.549-554
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• 2008

We study the multifractal spectrum of two dimensionally indexed classes whose members are distribution sets of a self-similar attractor in the unit interval.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.547-552
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• 2007

The unit interval is not homeomorphic to a self-similar Cantor set in which we studied the dimensions of distribution subsets. However we show that similar results regarding dimensions of the distribution subsets also hold for the unit interval since the distribution subsets have similar structures with those in a self-similar Cantor set.

• Korean Institute of Interior Design Journal
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• v.23 no.1
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• pp.88-95
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• 2014

This study intended arousal of other viewpoints that deal with and understand spaces and shapes, by describing the concept of 'dimensions' into visual patterns. Above all, the core concept of spatial dimensions was defined as 'expandability'. Then, first, the 'golden ratio', 'Fibonacci sequence', and 'fractal theory' were defined as elements of each dimension by stage. Second, a 'unit cell' of one dimension as 'minimum unit particles' was set. Next, Fibonacci sequence was set as an extended concept into two dimensions. Expansion into three dimensions was applied to the concept of 'self-similarity repetition' of 'Fractal'. In 'fractal dimension', the concept of 'regularity of irregularity' was set as a core attribute. Plus, Platonic solids were applied as a background concept of the setting of the 'unit cell' from the viewpoint of 'minimum unit particles'. Third, while 'characteristic patterns' which are shown in the courses of 'expansion' of each dimension were embodied for the visual expression forms of dimensions, expansion forms of dimensions are based on the premise of volume, directional nature, and concept of axes. Expressed shapes of each dimension are shown into visually diverse patterns and unexpected formative aspects, along with the expression of relative blank spaces originated from dualism. On the basis of these results, the 'unit cell' that is set as a concept of theoretical factor can be defined as a minimum factor of a basic algorism caused by other purpose. In here, by applying diverse pattern types, the fact that meaning spaces, shapes, and dimensions can be extracted was suggested.

• Journal of the Korean housing association
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• v.19 no.2
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• pp.43-54
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• 2008

The aim of the research is to find out the direction of unit-plans in multi-dwellings for the future society. Shinonome Canal Court where residents actually live now are the objects in this study, and the residential floor plan of unit-plans were analyzed to find out the typical types. The analysis was focused on the unit-plans of 5 blocks of Shinonome Canal Court. Space Syntax Theory was used as the analysis method. As the first stage of the analysis, justified graphs were made to find out the characters of unit-plans through the classification of the graphs. Contents of the analysis are as follows: Relationship between classified justified graphs and dimension according to node number. Relationship between classified justified graph patterns and unit-plans. Characters of unit-plans in each blocks. Shinonome Canal Court consists of mainly small scale unit-plans and 30unit-plans are classified. 1LDK, 2LDK, 1LDK+S, 1LDK+f are typical unit-plans which are mainly supplied in the complex. It is noted that the results of the analysis by node, justified graph pattern and dimension are the same. It also presents diverse unit-plans which shows a change in nLDK pattern or add f (foyer), AN (annex), S (service room), Fs (free space) to basic nLDK type. In summary, it demonstrates the possibility of creating new residental floor plans in multi-dwellings.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.497-506
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• 2019

Forecasting the U.S. employment level is made using machine learning methods of the artificial neural network: deep neural network, long short term memory (LSTM), gated recurrent unit (GRU). We consider the big data of the federal reserve economic data among which 105 important macroeconomic variables chosen by McCracken and Ng (Journal of Business and Economic Statistics, 34, 574-589, 2016) are considered as predictors. We investigate the influence of the two statistical issues of the dimension reduction and time series differencing on the machine learning forecast. An out-of-sample forecast comparison shows that (LSTM, GRU) with differencing performs better than the autoregressive model and the dimension reduction improves long-term forecasts and some short-term forecasts.