• Fibers and Polymers
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• v.6 no.4
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• pp.332-335
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• 2005

The fibrogram theory is newly derived from the superposition principle of the conventional staple diagram, in which the left-hand ends of the fibers have to share a common starting point in order for the fiber length distribution to be measured, and the right-hand ends of the fibers form points. It is shown that the fibrogram is the staple diagram of the fiber sample having different random starting points, as well as the double cumulative distribution function of the frequency length function in the length biased sample. Also, the various means, viz. the numerical mean length, numerical mean length in median, length biased mean length, and length biased mean length in median, and the various upper half means, viz. the numerical upper half mean length, numerical upper half mean length in median, length biased upper half mean length, and length biased upper half mean length in median, are discussed in relation to the cotton blending process.

• The Journal of the Petrological Society of Korea
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• v.20 no.1
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• pp.23-37
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• 2011

The scaling properties on the length distribution of microcrack populations from Tertiary crystalline tuff are investigated. From the distribution charts showing length range with 15 directional angles and five groups(I~V), a systematic variation appears in the mean length with microcrack orientation. The distribution charts are distinguished by the bilaterally symmetrical pattern to nearly N-S direction. The whole domain of the length-cumulative frequency diagram for microcrack populations can be divided into three sections in terms of phases of the distribution of related curves. Especially, the linear middle section of each diagram of five groups represents a power-law distribution. The frequency ratio of linear middle sections of five groups ranges from 46.6% to 67.8%. Meanwhile, the slope of linear middle section of each group shows the order: group V($N60{\sim}90^{\circ}E$, -2.02) > group IV($N20{\sim}60^{\circ}E$, -1.55) > group I($N60{\sim}90^{\circ}W$, -1.48), group II($N10{\sim}60^{\circ}W$, -1.48) > group III($N10^{\circ}W{\sim}N20^{\circ}E$, -1.06). Five sub-populations(five groups) that closely follow the power-law length distribution show a wide range in exponents( -1.06 - -2.02). These differences in exponent among live groups emphasizes the importance of orientation effect. In addition, breaks in slope in the lower parts of the related curves represent the abrupt development of longer lengths, which is reflected in the decrease in the power-law exponent. Especially, such a distribution pattern can be seen from the diagram with $N10{\sim}20^{\circ}E,\;N10{\sim}20^{\circ}W$ and $N60{\sim}70^{\circ}W$ directional angles. These three directional angles correspond with main directions of faults developed around the study area. The distribution chart showing the individual characteristics of the length-cumulative frequency diagrams for 15 directional angles were made. By arraying above diagrams according to the categories of three groups(A, B and C), the differences in length-frequency distributions among these groups can be easily derived. The distribution chart illustrates the importance of analysing microcrack sets separately. From the related chart, the occurrence frequency of shorter microcracks shows the order: group A > group B > group C. These three types of distribution patterns could reveal important information on the processes occurred during microcrack growth.

• The Journal of the Petrological Society of Korea
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• v.24 no.3
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• pp.165-180
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• 2015

Jurassic granite from Geochang was analysed with respect to the characteristics of the rock cleavage. The phases of distribution of microcracks were well evidenced from the enlarged photomicrographs(${\times}6.7$) of the thin section. In this study, the length - cumulative frequency diagrams were used for expressing the distribution characteristics of microcrack. The diagrams for the six directions were arranged in the magnitude of density(${\rho}$). These diagrams show an order of H2 < H1 < G2 < G1 < R2 < R1 from the related chart. Among six diagrams, the diagram for hardway 2(H2) occupies the lowermost region on the left. On the contrary, the diagram for rift 1(R1) occupies the uppermost region on the right. Curve patterns of the two diagrams change from uniform to exponential distribution type in accordance with the increased density. The overall distribution characteristics of the diagrams were well evidenced from the magnitude of the exponent(${\lambda}$) and length of line oa related to the exponential straight line. The magnitude of exponent governing the values of slope(${\theta}$) is inversely proportional to the values of microcrack parameters such as number(N), length(L) and density. On the contrary, length of line oa is directly proportional to the values of the above three parameters. Above microcrack parameters related to the order of arrangement of diagrams show an order of hardway(H1 + H2) < grain(G1 + G2) < rift(R1 + R2). The distribution characteristics of progressive variation are found among the six diagrams. The order of arrangement of the diagrams indicates a relative magnitude of the rock cleavage. Meanwhile, the parameters such as slope, exponent, density and length of line oa were arranged in an order of H2 < H1 < G2 < G1 < R2 < R1. The variation curves of a smooth quadratic function are shown from the related chart. From the correlation chart between density and the above parameters, a common regularity following power-law correlation function was derived. Finally, the analysis for the rock cleavage was conducted through the combination between the diagram and microcrack parameter. This type of combination contribute to the progressivity in evaluation for the rock cleavage.

• The Journal of the Petrological Society of Korea
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• v.19 no.2
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• pp.123-139
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• 2010

The properties of fracture system in Precambrian Jangbong schist and Mesozoic granites from Seokmo-do, Ganghwa-gun were investigated and analyzed. Most of the fractures measured at outcrops are nearly vertical or steeply dipping. Orientations of fracture sets in terms of frequency order are as follows: Set $1:N2^{\circ}E/77^{\circ}SE$, Set $2:N17^{\circ}E/84^{\circ}NW$, Set $3:N26^{\circ}E/64^{\circ}SE$, Set $4:N86^{\circ}W/82^{\circ}SW$, Set $5:N80^{\circ}W/77^{\circ}NE$, Set $6:N60^{\circ}W/85^{\circ}SW$, Set $7:N73^{\circ}E/87^{\circ}NW$, Set $8:N82^{\circ}W/53^{\circ}NE$, Set $9:N23^{\circ}W/86^{\circ}SW$, Set 10: $N39^{\circ}W/61^{\circ}NE$. Especially, the rose diagram of fracture strikes(N:240) indicates that there are two dorminant directions of N-S~NNE and WNW. These distribution pattern of fractures from Seokmo-do correponds with those of major lineaments from South Korea suggested in previous study. Meanwhile, the scaling properties on the length distribution of fracture populations have been investigated. First, fracture sets from Precambrian Jangbong schist and Mesozoic granites(north and south rock body) has been classified into five groups(group I~V) based on strike and frequency. Then, the distribution chart generalized the individual length-cumulative frequency diagram for above five groups were made. From the related chart, five subpopulations(group I~V) that closely follow a power-law length distribution show a wide range in exponents(-0.79~-1.53). These relative differences in exponent among five groups emphasizes the importance of orientation effect. From the related chart, the diagram of group III occupies an upper region among five groups. Finally, the distribution chart showing the chracteristics of the length frequency distribution for each rock body were made. From the related chart, the diagram of each rock body shows an order of porphyritic biotite granite < hornblende granodiorite < medium-grained biotite granite(south rock body) < medium-grained biotite granite(north rock body) < Precambrian Jangbong schist. From the related chart, the diagram of more older rock body in the formation age tends to occupy an upper region. Especially, the diagram of Precambrian Jangbong schist occupies an upper region compared with the diagrams of Mesozoic granites. These distributional chracteristics suggests that coexistence of new fracture initiation and growing of existing fractures corresponding with stress field acted since the formation of rock body.

• Journal of The Korean Astronomical Society
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• v.55 no.3
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• pp.75-86
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• 2022

The lunar surface progressively darkens and reddens as a result of sputtering from solar wind particles and bombardment of micrometeoroids. The extent of exposure to these space weathering agents is frequently calculated as the location in a diagram of reflectance at 750 nm vs. 950 nm/750 nm color (R-C). Sim & Kim (2018) examined the R-C trends of pixels within ~3,500 craters, and revealed that the length (L) and skewness (s) of R-C trends can be employed as a secondary age or maturity indicator. We broaden this research to general lunar surface areas (3,400 tiles of 0.25° × 0.25° size) in 218 mare basalt units, whose ages have been derived from the size-frequency distribution analysis by Hiesinger et al. (2011). We discover that L and s rise with age until ~3.2 Gyr and reduce rather rapidly afterward, while the optical maturity, OMAT, reduces monotonically with time. We show that in some situations, when not only OMAT but also L and s are incorporated in the estimation utilizing 750 & 950 nm photometry, the age estimation becomes considerably more reliable. We also observed that OMAT and the lunar cratering chronology function (cumulative number of craters larger than a certain diameter as a function of time) have a relatively linear relationship.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.48.2-48.2
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• 2021

The lunar surface progressively darkens and reddens as a result of sputtering from solar wind particles and bombardment of micrometeoroids. The extent of exposure to these space weathering agents is frequently calculated as the location in a diagram of reflectance at 750 nm vs. 950 nm/750 nm color (R-C). Sim & Kim (2018) examined the R-C trends of pixels within ~3,500 craters, and revealed that the length (L) and skewness (s) of R-C trends can be employed as a secondary age or maturity indicator. We broaden this research to general lunar surface areas (3,400 tiles of 0.25° × 0.25° size) in 218 mare basalt units, whose ages have been derived from the size-frequency distribution analysis by Hiesinger et al. (2011). We discover that L and s rise with age until ~3.2 Gyr and reduce rather rapidly afterward, while the optical maturity, OMAT, reduces monotonically with time. We show that in some situations, when not only OMAT but also L and s are incorporated in the estimation utilizing 750 & 950 nm photometry, the age estimation becomes considerably more reliable. We also observed that OMAT and the lunar cratering chronology function (cumulative number of craters larger than a certain diameter as a function of time) have a relatively linear relationship.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.203-212
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• 2018

Quality requirements of manufactured products or parts are given in the form of specification limits on the quality characteristics of individual units. If a product is to meet the customer's fitness for use criteria, it should be produced by a process which is stable or repeatable. In other words, it must be capable of operating with little variability around the target value or nominal value of the product's quality characteristic. In order to maintain and improve product quality, we need to apply statistical process control techniques such as histogram, check sheet, Pareto chart, cause and effect diagram, or control charts. Among those techniques, the most important one is control charting. The cumulative sum (CUSUM) control charts have been used in statistical process control (SPC) in industries for monitoring process shifts and supporting online measurement. The objective of this research is to apply Taguchi's quality loss function concept to cost based CUSUM control chart design. In this study, a modified quality loss function was developed to reflect quality loss situation where general quadratic loss curve is not appropriate. This research also provided a methodology for the design of CUSUM charts using Taguchi quality loss function concept based on the minimum cost per hour criterion. The new model differs from previous models in that the model assumes that quality loss is incurred even in the incontrol period. This model was compared with other cost based CUSUM models by Wu and Goel, According to numerical sensitivity analysis, the proposed model results in longer average run length in in-control period compared to the other two models.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.12
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• pp.77-87
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• 1972

The fruiting phase of rape under transplanting and direct-sowing conditions has been studied at Mokpo during the 2 years period from 1970 to 1971. Two varieties, Yudal and Miyuki were used in this study. The planting space and sowing time were also incorporated into this study. The results could be summarized as follows: 1. The plant tape of rape was nearly umbrella-shaped of all, but has changed to the laid elliptical-shaped, broadly ovate and spindle-shaped under different varieties and cultural conditions in the plant diagram(Fig. 2). 2. The length of the primary branches for each nodes had a tendency to the symmetric apical curve with the apex at the upper 10-12th node in the transplanting. but to the upper bias apical curve with the apex at the upper 5-7th node in the dense-sowing(Fig.3). 3. The ear of main stem was longer, more pods, heavier 1, 000 grains and more grain yield than ear of primary branches of all, Especially, as for that, the rate of yield constitution per plant in the direct-sowing was higher than in the transplanting(Fig. 4, 5, 6, 7, 8, 9). 4. The ear-length of the primary branches for each nodes had a tendency to the relatively slowly apical curve with the apex at the upper 3-4th node in the transplanting, but to the lower bias apical curve with the apex at the upper 2nd node in the dense-sowing. Especially, the possibility of growth at the lower ears was few in the early variety (Fig. 4). 5. The number of pod per ear on the primary branches for each nodes had a .tendency to the curve of ear-length with the apex at the upper 5-8thnode in the transplanting and at the upper 4-5th node in the dense-sowing (Fig. 5). Accordingly, a high positive correlation was found between the ear-length and number of pod per ear (Table 2) 6. In the transplanting, the high rate of effective ear was from the upper nods to the 12th node, but below the 16-17th nodes was ineffective. However, in the early dense-sowing the high rate of effective was to the 7th node. but below the 10th nodes was. ineffective. Especially, in the early variety has difficult to secure of poi-numbers for ineffective of the lower nodes(Fig. 6.). 7. The density of pod setting of the ear of main stem was the longest of all ears, and the lower nods were, the shorter it became. That had a tendency to the evidently apical growth. However. in the early variety, it was lengthened according to growth of ear-length(Fig.7). 8. The pod-length of the medium nodes was longer than the upper and lower, and the possitive correlation between pod-length and number of grain per poi was very high(Table 2.). 9. In the grain yield per node of primary branches, the most yielding node of transplanting was the upper 9th node, of dense-sowing 4-5th node(Fig 8.), and the possitive correlation between grain yield per node and ear-length or number of pod per ear was very high(Table 2). 10. The grain yield of ear of main stem was higher than that of primary branches in the percentage of dependence for grain yield per plant. The limint node of 50% of dependence to cumulative grain yield per plant was the upper 7-8th node in tranplanting, in the early dense-sowing 4-5th node, and in tke late dense-sowing-3th node(Fig. 9). 11. In the weight of 1, 000 grains the lower nodes were, the lighter it becames in dense-sowing. Therefore, this was also lighter than in the transplanting to the (Fig. 10.). 12. The oil content of grain at the medium nodes was low in the early variety, but at the ear of main stem and upper 1st node it was extremely high(Fig. 11.).

• The Journal of the Petrological Society of Korea
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• v.25 no.1
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• pp.13-27
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• 2016

The characteristics of the rock cleavage inherent in Jurassic granite from Geochang were analysed. The phases of distribution of microcrack spacings were derived from the enlarged photomicrographs(${\times}6.7$) of the thin section. The evaluation for the six directions of rock cleavages was performed using nine parameters such as (1) frequency of microcrack spacing(N), (2) frequency ratio(${\leq}1mm$ and 4 mm >) to total spacing frequency(N:191), (3) spacing ratio(${\leq}1mm$) to total spacing(118.49 mm), (4) mean spacing($S_{mean}$), (5) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$), (6) density of spacing, (7) median spacing, (8) reduction ratio of spacing frequency to length frequency and (9) magnitude of exponent(${\lambda}$ and b) related to the distribution type of diagram. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of (I) parameters(1, 2 and 3), (II) parameters(4, 5 and 6), (III) parameter(7), (IV) parameter(8) and (V) parameter(9) show the various orders of H(hardway, H1+H2) < G(grain, G1+G2) < R(rift, R1+R2), R < G < H, R < H < G, G < H < R and H < G < R, respectively. On the contrary, the values of the above four groups(I~IV) of parameters for three planes show reverse orders. This type of correlation analysis is useful for discriminating three quarrying planes. Six spacing-cumulative frequency diagrams were arranged in increasing order on the value of main parameter($S_{mean}-S_{median}$). These diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, the above six diagrams can be summarized in order of rift(R1+R2) < grain(G1+G2) < hardway(H1+H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, the above main parameter could provide advanced information for prediction the order of arrangement among the diagrams.

• The Journal of the Petrological Society of Korea
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• v.25 no.4
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• pp.311-324
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• 2016

The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for three quarrying planes and three rock cleavages was performed using the parameters such as (1) reduction ratio between the value of spacing and the value of length, (2) microcrack spacing frequency(N), (3) total spacing($1mm{\geq}$), (4) exponential constant(a), (5) magnitude of exponent(${\lambda}$), (6) mean spacing($S_{mean}$), (7) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$) and (8) density of spacing. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The discrimination factors representing three quarrying planes and three rock cleavages were acquired through these mutual contrast. The analysis results of the research are summarized as follows. First, the reduction ratios of frequency(N), mean value, median value, the above difference value($S_{mean}-S_{median}$) and density for three rock cleavages are in orders of G(grain, (G1 + G2)/2) < H(hardway, (H1 + H2)/2) < R(rift, (R1 + R2)/2), H < G $\ll$ R, H < G $\ll$ R, H < G < R and H < G $\ll$ R. The values of the above five parameters for three planes show the various orders of R'(rift plane) $\ll$ H'(hardway plane) < G'(grain plane), R' $\ll$ G' < H', R' < H' < G', R' < G' < H' and R' $\ll$ H' < G', respectively. Second, the values of (I) parameters(2, 3, 4 and 5) and (II) parameters(6, 7 and 8) are in orders of (I) H < G < R and (II) R < G < H. On the contrary, the values of the above two groups(I~II) of parameters for three planes show reverse orders. Third, to review the overall characteristics of the arrangement among the six diagrams, these diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, above six diagrams can be summarized in order of rift(R1 + R2) < grain(G1 + G2) < hardway(H1 + H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, two parameters for each diagram, the above difference value($S_{mean}-S_{median}$) and mean spacing, could provide advanced information for prediction the order of arrangement among the diagrams. Finally, the general chart for three planes and three rock cleavages were made. From the related chart, three exponential straight lines for three rock cleavages show an order of R(R1 + R2) < G(G1 + G2) < H(H1 + H2). On the contrary, three lines for three planes show an order of H'(R2 + G2) < G'(R1 + H2) < R'(G1 + H1). Consequently, correlation of the mutually reverse order between three planes and three rock cleavages can be drawn from the related chart.