• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.29-51
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• 2003

In this paper we construct a natural filtration associated to the plethysm $S_{r}(\wedge^2 \varphi)$ over arbitrary commutative ring R. Let $\phi$ : G longrightarrow F be a morphism of finite free R-modules. We construct the natural filtration of $S_{r}(\wedge^2 \varphi)$ as a $GL(F){\times}GL(G)$- complex such that its associated graded complex is ${\Sigma}_{{\lambda}{\in}{\Omega}_{\gamma}}=L_{2{\lambda}{\varphi}$, where ${{\Omega}_{\gamma}}^{-}$ is a set of partitions such that $│\wedge│\;=;{\gamma}\;and\;2{\wedge}$ is a partition of which i-th term is $2{\wedge}_{i}$. Specializing our result, we obtain the filtrations of $S_{r}(\wedge^2 F)\;and\;D_{r}(D_2G).

• Imaging Science in Dentistry
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• v.48 no.2
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• pp.97-101
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• 2018

Purpose: This study evaluated the radiopacity of contemporary luting cements using conventional and digital radiography. Materials and Methods: Disc specimens (N=24, n=6 per group, ø$7mm{\times}1mm$) were prepared using 4 resin-based luting cements (Duolink, Multilink N, Panavia F 2.0, and U-cem). The specimens were radiographed using films, a complementary metal oxide semiconductor (CMOS) sensor, and a photostimulable phosphor plate (PSP) with a 10-step aluminum step wedge (1 mm incremental steps) and a 1-mm-thick tooth cut. The settings were 70 kVp, 4 mA, and 30 cm, with an exposure time of 0.2 s for the films and 0.1 s for the CMOS sensor and PSP. The films were scanned using a scanner. The radiopacity of the luting cements and tooth was measured using a densitometer for the film and NIH ImageJ software for the images obtained from the CMOS sensor, PSP, and scanned films. The data were analyzed using the Kruskal-Wallis and Mann-Whitney U tests. Results: Multilink (3.44-4.33) showed the highest radiopacity, followed by U-cem (1.81-2.88), Panavia F 2.0 (1.51-2.69), and Duolink (1.48-2.59). The $R^2$ values of the optical density of the aluminum step wedge were 0.9923 for the films, 0.9989 for the PSP, 0.9986 for the scanned films, and 0.9266 for the CMOS sensor in the linear regression models. Conclusion: The radiopacities of the luting materials were greater than those of aluminum or dentin at the same thickness. PSP is recommended as a detector for radiopacity measurements because of its accuracy and convenience.

• Journal of Food Hygiene and Safety
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• v.26 no.2
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• pp.120-124
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• 2011

Predictive mathematical models were developed for predicting the kinetics of growth of Listeria monocytogenes in smoked salmon, which is the popular ready-to-eat foods in the world, as a function of temperature (4, 10, 20 and $30^{\circ}C$). At these storage temperature, the primary growth curve fit well ($r^2$=0.989~0.996) to a Gompertz equation to obtain specific growth rate (SGR) and lag time (LT). The Polynomial model for natural logarithm transformation of the SGR and LT as a function of temperature was obtained by nonlinear regression (Prism, version 4.0, GraphPad Software). Results indicate L. monocytogenes growth was affected by temperature mainly, and SGR model equation is $365.3-31.94^*Temperature+0.6661^*Temperature^{\wedge^2}$ and LT model equation is $0.1162-0.01674^*Temperature+0.0009303^*Temperature{\wedge^2}$. As storage temperature decreased $30^{\circ}C$ to $4^{\circ}C$, SGR decreased and LT increased respectively. Polynomial model was identified as appropriate secondary model for SGR and LT on the basis of most statistical indices such as bias factor (1.01 by SGR, 1.55 by LT) and accuracy factor (1.03 by SGR, 1.58 by LT).

• Geotechnical Engineering
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• v.13 no.3
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• pp.101-122
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• 1997

A spiting reinforcement system is composed of a series of radially installed reinforcing spites along the perimeter of the tunnel opening ahead of excavation. The reinforcing spill network is extended into the in-situ soil mass both radially and longitudinally The sailing reinforcement system has been successfully used for the construction of underground openings to reinforce weak rock formations on several occasions. The application of this spiting reinforcement system is currently extended to soft ground tunneling in limited occasions because of lack of reliable analysis and design methods. A method of threetimensional limit equilibrium stability analysis of the smile-reinforced shallow tunnel in soft ground is presented. The shape of the potential failure wedge for the case of smile-reinforced shallow tunnel is assumed on the basis of the results of three dimensional finite element analyses. A criterion to differentiate the spill-reinforced shallow tunnel from the smile-reinforced deep tunnel is also formulated, where the tunnel depth, soil type, geometry of the tunnel and reinforcing spites, together with soil arching effects, are considered. To examine the suitability of the proposed method of threedimensional stability analysis in practice, overall stability of the spill-reinforced shallow tunnel at facing is evaluated, and the predicted safety factors are compared with results from twotimensional analyses. Using the proposed method of threetimensional limit equilibrium stability analysis of the smile-reinforced shallow tunnel in soft ground, a parametric study is also made to investigate the effects of various design parameters such as tunnel depth, smile length and wadial spill spacing. With slight modifications the analytical method of threeiimensional stability analysis proposed may also be extended for the analysis and design of steel pipe reinforced multi -step grouting technique frequently used as a supplementary reinforcing method in soft ground tunnel construction.